1-7 inverse relations and...

Graph each function using a graphing calculator, and apply the horizontal line test to determine whether its inverse function exists. Write yes or no.

1. f (x) = x2 + 6x + 9

SOLUTION:

The graph of f (x) = x2 + 6x + 9 below shows that it is possible to find a

horizontal line that intersects the graph of f (x) more than once. Therefore, you can conclude that an inverse function does not exist.

2. f (x) = x2 – 16x + 64

SOLUTION:

The graph of f (x) = x2 – 16x + 64below shows that it is possible to find

a horizontal line that intersects the graph of f (x) more than once. Therefore, you can conclude that an inverse function does not exist.

3. f (x) = x2 – 10x + 25

SOLUTION:

The graph of f (x) = x2 – 10x + 25 below shows that it is possible to find

4. f (x) = 3x − 8

SOLUTION:

It appears from the portion of the graph of f (x) = 3x − 8 shown below that there is no horizontal line that intersects the graph of f (x) more thanonce. Therefore, you can conclude that an inverse function does exist.

5. f (x) =

SOLUTION:

It appears from the portion of the graph of f (x) = shown below that there is no horizontal line that intersects the graph of f (x) more than

once. Therefore, you can conclude that an inverse function does exist.

6. f (x) = 4

SOLUTION: The graph of f (x) = 4 below shows that it is possible to find a horizontal line that intersects the graph of f (x) more than once. That horizontal lineis the same as the graph of f (x) itself. Therefore, you can conclude thatan inverse function does not exist.

7. f (x) =

SOLUTION:

It appears from the portion of the graph of f (x) = shown belowthat there is no horizontal line that intersects the graph of f (x) more thanonce. Therefore, you can conclude that an inverse function does exist.

8. f (x) = −4x2 + 8

SOLUTION:

The graph of f (x) = −4x2 + 8 below shows that it is possible to find a

9. f (x) =

SOLUTION:

It appears from the portion of the graph of f (x) = shown below

that there is no horizontal line that intersects the graph of f (x) more thanonce. Therefore, you can conclude that an inverse function does exist.

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

It appears from the portion of the graph of f (x) = x3 – 9 shown below

12. f (x) = x3

SOLUTION:

It appears from the portion of the graph of f (x) = x3 shown below

Determine whether f has an inverse function. If it does, find the inverse function and state any restrictions on its domain.

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

The graph of g(x) = −3x4 + 6x

2 – x below shows that it is possible to

find a horizontal line that intersects the graph of g(x) more than once. Therefore, you can conclude that an inverse function does not exist.

14. f (x) = 4x5 – 8x

SOLUTION:

The graph of f (x) = 4x5 – 8x

4 below shows that it is possible to find a

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

The graph of h(x) = x7 + 2x

3 − 10x2 below shows that it is possible to

find a horizontal line that intersects the graph of h(x) more than once. Therefore, you can conclude that an inverse function does not exist.

16. f (x) =

SOLUTION:

The function f has domain [–8, ) and range [0, ).

(x) = x2 − 8

From the graph y = x2 – 8 below, you can see that the inverse relation

has domain (– , ) and range [8, ).

By restricting the domain of the inverse relation to [0, ), the domain

and range of f are equal to the range and domain of f –1

, respectively.

Therefore, f −1(x) = x

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

The graph of f (x) = below shows that it is possible to find a horizontal line that intersects the graph of f (x) more than once. Therefore, you can conclude that an inverse function does not exist.

18. f (x) = | x – 6 |

SOLUTION: The graph of f (x) = | x – 6 | below shows that it is possible to find a horizontal line that intersects the graph of f (x) more than once. Therefore, you can conclude that an inverse function does not exist.

19. f (x) =

SOLUTION:

The function f has domain (– , 0) (0, ) and range [– , –1)

(–1, ).

f–−1

From the graph y = below, you can see that the inverse relation

has domain (– , –1) (–1, ) and range (– , 0) (0, ).

The domain and range of f are equal to the range and domain of f –1

respectively. Therefore, no further restrictions are necessary. f –−1(x)

= for x ≠ −1.

20. g(x) =

SOLUTION:

It appears from the portion of the graph of g(x) = shown below

that there is no horizontal line that intersects the graph of g(x) more than once. Therefore, you can conclude that an inverse function does exist.

The function g has domain (– , 0) (0, ) and range [– , 1)

(1, ).

g−1(x) =

has domain [– , 1) (1, ) and range (– , 0) (0, ).

The domain and range of g are equal to the range and domain of g –1

respectively. Therefore, no further restrictions are necessary. g–−1(x)

= for x ≠ 1.

21. f (x) =

SOLUTION:

The function f has domain (– , 8) and range (0, ).

f–−1

(x) = 8 − .

has domain [– , 0) (0, ) and range (– , 8).

By restricting the domain of the inverse relation to (0, ∞), the domain

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

It appears from the portion of the graph of g(x) = shown

below that there is no horizontal line that intersects the graph of g(x) more than once. Therefore, you can conclude that an inverse function does exist.

The function g has domain (–3, ) and range (0, ).

g−1(x) = −3 +

From the graph y = −3 + below, you can see that the inverse

relation has domain (– , 0) (0, ) and range (–3, ).

By restricting the domain of the inverse relation to (0, ), the domain

and range of g are equal to the range and domain of g –1

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

The function f has domain (– , 8) (8, ) and range (– , 6)

(6, ).

f–−1

has domain (– , 6) (6, ) and range (– , 8) (8, ).

respectively. Therefore, no further restrictions are necessary. f –−1(x) =

for x 6.

24. h(x) =

SOLUTION:

It appears from the portion of the graph of h(x) = shown below

that there is no horizontal line that intersects the graph of h(x) more than once. Therefore, you can conclude that an inverse function does exist.

The function h has domain and range

has domain and range .

The domain and range of h are equal to the range and domain of h –1

respectively. Therefore, no further restrictions are necessary. h−1(x) =

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: The graph of g(x) = | x + 1 | + | x – 4 || below shows that it is possible to find a horizontal line that intersects the graph of g(x) more than once.Therefore, you can conclude that an inverse function does not exist.

26. SPEED The speed of an object in kilometers per hour y is y = 1.6x, where x is the speed of the object in miles per hour. a. Find an equation for the inverse of the function. What does each variable represent? b. Graph each equation on the same coordinate plane.

SOLUTION: a.

y = speed in mi/h, x = speed in km/hb.

Show algebraically that f and g are inverse functions.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

37. PHYSICS The kinetic energy of an object in motion in joules can be

described by f (x) = 0.5mx2, where m is the mass of the object in

kilograms and x is the velocity of the object in meters per second. a. Find the inverse of the function. What does each variable represent? b. Show that f (x) and the function you found in part a are inverses.

c. Graph f (x) and f –1

(x) on the same graphing calculator screen if the mass of the object is 1 kilogram.

SOLUTION: a.

g(x) = velocity in m/s, x = kinetic energy in joules, m = mass in kg b.

Because = = x, the functions are inverse when the domain

is restricted to [0, ).

Use the graph of each function to graph its inverse function.

SOLUTION: Graph the line y = x and reflect the points. Then connect the points witha smooth curve that resembles the original graph.

44. JOBS Jamie sells shoes at a department store after school. Her base salary each week is $140, and she earns a 10% commission on each pair of shoes that she sells. Her total earnings f (x) for a week in which she sold x dollars worth of shoes is f (x) = 140 + 0.1x.

a. Explain why the inverse function f −1(x) exists. Then find f −1

b. What do f −1(x) and x represent in the inverse function?

c. What restrictions, if any, should be placed on the domains of f (x) and

f −1

(x)? Explain.

d. Find Jamie’s total sales last week if her earnings for that week were $220.

SOLUTION: a. Sample answer: The graph of the function is linear, so it passes the horizontal line test. Therefore, it is a one-to-one function and it has an inverse.

f −1(x) = 10x − 1400

b. x represents Jamie’s earnings for a week, and f −1(x) represents her

sales. c. x ≥ 0; Jamie cannot have negative sales. d.

45. CURRENCY The average exchange rate from Euros to U.S. dollars for a recent four-month period can be described by f (x) = 0.66x, where x is the currency value in Euros.

f −1

(x)? Explain.

d. What is the value in Euros of 100 U.S. dollars?

b. x represents the value of the currency in U.S. dollars, and f −1(x)

represents the value of the currency in Euros. c. x ≥ 0; You cannot exchange negative money. d.

Determine whether each function has an inverse function.

SOLUTION: The graph does not pass the Horizontal Line Test.

SOLUTION: The graph passes the Horizontal Line Test.

Determine if f −1 exists. If so, complete a table for f −1.

SOLUTION: No output value corresponds with more than one input value, so an inverse exists.

SOLUTION: An output value corresponds with more than one input value, so an inverse does not exist.

54. TEMPERATURE The formula f (x) = x + 32 is used to convert x

degrees Celsius to degrees Fahrenheit. To convert x degrees

Fahrenheit to Kelvin, the formula k(x) = (x + 459.67) is used.

a. Find f −1. What does this function represent?

b. Show that f and f −1 are inverse functions. Graph each function on the same graphing calculator screen. c. Find (k o f )(x).What does this function represent? d. If the temperature is 60°C, what would the temperature be in Kelvin?

SOLUTION: a.

f −1 represents the formula used to convert degrees Fahrenheit to

degrees Celsius. b.

[k o f ](x) = x + 273.15; represents the formula used to convert degrees Celsius to degrees Kelvin. d.

Restrict the domain of each function so that the resulting function is one-to-one. Then determine the inverse of the function.

SOLUTION: The domain needs to be restricted so that the graph passes the Horizontal Line Test. There is more than one way to accomplish this.

Sample answer: x ≥ 5

f −1 (x) = + 5

Sample answer: x ≤ −9

We are selecting the negative side of the domain, so we will replace the absolute value symbols with the opposite of the expression.

f −1 (x) = x – 11

Since the range of the restricted function f is y ≤ –2, we must restrict

the inverse relation so that the domain is x ≤ 2. Therefore, f −1 (x) = x –11.

SOLUTION: The domain needs to be restricted so that the graph passes the Horizontal Line Test. There is more than one way to accomplish this. Sample answer: x ≥ 0

We are using the positive side of the domain, so we only need the positive value of y .

Sample answer: x ≥ −5

We are selecting the positive side of the domain, so we will replace the absolute value symbols with the expression.

(x) = x – 1

Since the range of the restricted function f is y ≥ –4, we must restrict

the inverse relation so that the domain is x ≥ –4. Therefore, f −1 (x) = x

– 1, x ≥ –4.

State the domain and range of f and f −1, if f −1 exists.

59. f (x) =

SOLUTION: For f , the square root must be at least 0, so x must be greater than or equal to 6. f: D = x | x ≥ 6, x R, R = y | y ≥ 0, y R

Graph f .

The graph of f passes the Horizontal Line Test, so f −1 exists.

By restricting the domain of f−1 to [0, ∞], the range becomes [6, ∞].

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

f −1 does not exist

61. f (x) =

SOLUTION: Graph f .

There appears to be asymptotes at x = 4 and y = 3. f: D = x | x 4, x R, R = y | y 3, x R

The domain and range restrictions of f correspond with the range and

domain restrictions of f−1

. Therefore, no further restrictions are needed.

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

63. ENVIRONMENT Once an endangered species, the bald eagle was downlisted to threatened status in 1995. The table shows the number of nesting pairs each year.

a. Use the table to approximate a linear function that relates the numberof nesting pairs to the year. Let 0 represent 1984. b. Find the inverse of the function you generated in part a. What does each variable represent? c. Using the inverse function, in approximately what year was the number of nesting pairs 5094?

SOLUTION: a. Use two points from the table to write the related equation of the function. Because x = 0 corresponds to 1984, two points that can be used are (0, 1757) and (21, 7066). First, find the slope of the line.

One of the points chosen is (0, 1757), so the y-intercept is 1757. So, the related equation is y = 252.81x + 1757. Therefore, a linear function that can be used to relate the number of nesting pairs to the year is f (x) = 252.81x + 1757. b.

An inverse function is f −1(x) = , where x represents the

number of nesting pairs and f −1(x) represents the number of years

after 1984.

c. Substitute 5094 for x in f––1

Because x = 0 corresponds to 1984, 13.20 corresponds to 1984 + 13.2 or about 1997.2. Therefore, the number of nesting pairs was 5094 in 1997.

64. FLOWERS Bonny needs to purchase 75 flower stems for banquet decorations. She can choose between lilies and hydrangea, which cost $5.00 per stem and $3.50 per stem, respectively. a. Write a function for the total cost of the flowers. b. Find the inverse of the cost function. What does each variable represent? c. Find the domain of the cost function and its inverse. d. If the total cost for the flowers was $307.50, how many lilies did Bonny purchase?

SOLUTION: a. Let x represent the number of stems of hydrangea; b.

c(x) = 3.5x + 5(75 − x).

c −1(x) = 250 − ; x represents the total cost and c

−1(x) represents

the number of stems of hydrangea c. Bonny is not purchasing more than 75 stems. Therefore, the domain

of c(x) is x | 0 ≤ x ≤ 75, x ∈ R. The range of c(x) is from c(0) to c(75).

The domain of c −1(x) is equal to the range of c(x), or x | 262.5 ≤ x ≤

375, x ∈R

Remember that x is the number of hydrangea. The number of lilies is

75 − 45 or 30.

Find an equation for the inverse of each function, if it exists. Then graph the equations on the same coordinate plane. Includeany domain restrictions.

SOLUTION: The range of the first equation is y ≥ 16, which is equivalent to the

domain of f−1

The domain of f (x) is for negative values of x, so the inverse of f (x) =

x2 is f

−1(x) = − .

The range of the second equation is y < 13, which is equivalent to the

domain of f−1

SOLUTION:

The graph of f (x) does not pass the Horizontal Line Test. Therefore, f −1 does not exist.

67. FLOW RATE The flow rate of a gas is the volume of gas that passes through an area during a given period of time. The velocity v of air

flowing through a vent can be found using v(r) = , where r is the

flow rate in cubic feet per second and A is the cross-sectional area of the vent in square feet.

a. Find v

−1 of the vent shown. What does this function represent?

b. Determine the velocity of air flowing through the vent in feet per

second if the flow rate is 15,000 .

c. Determine the gas flow rate of a circular vent that has a diameter of

5 feet with a gas stream that is moving at 1.8 .

SOLUTION:

a. The cross section is a rectangle 2 ft by 1.5 ft. So, v(r) = and v−1

(x) = 3x. This represents the formula for the flow rate of the gas. b. The velocity of air flowing through the vent in feet per second

c. The cross sectional area is π(2.5)2 or 6.25π. So, v(r) = and

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

68. COMMUNICATION A cellular phone company is having a sale as shown. Assume the $50 rebate only after the 10% discount is given.

a. Write a function r for the price of the phone as a function of the original price if only the rebate applies. b. Write a function d for the price of the phone as a function of the original price if only the discount applies. c. Find a formula for T(x) = [r d](x) if both the discount and the rebate apply.

d. Find T −1 and explain what the inverse represents.

e . If the total cost of the phone after the discount and the rebate was $49, what was the original price of the phone?

SOLUTION: a. r(x) = x − 50 b. d(x) = 0.9x c. The discount comes before the rebate, so T(x) = 0.9x − 50. d.

The inverse represents the original price of the phone as a function of the price of the phone after the rebate and the discount. e .

Use f (x) = 8x – 4 and g (x) = 2x + 6 to find each of the following.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

Now, find the inverse.

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

eSolutions Manual - Powered by Cognero Page 1

1-7 Inverse Relations and Functions

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

1. f (x) = x2 + 6x + 9

SOLUTION:

2. f (x) = x2 – 16x + 64

SOLUTION:

3. f (x) = x2 – 10x + 25

SOLUTION:

4. f (x) = 3x − 8

SOLUTION:

5. f (x) =

SOLUTION:

6. f (x) = 4

7. f (x) =

SOLUTION:

8. f (x) = −4x2 + 8

SOLUTION:

9. f (x) =

SOLUTION:

10. f (x) =

SOLUTION:

11. f (x) = x3 – 9

SOLUTION:

12. f (x) = x3

SOLUTION:

13. g(x) = −3x4 + 6x

2 – x

SOLUTION:

14. f (x) = 4x5 – 8x

SOLUTION:

15. h(x) = x7 + 2x

3 − 10x2

SOLUTION:

16. f (x) =

SOLUTION:

(x) = x2 − 8

, respectively.

2 − 8 for x ≥ 0.

17. f (x) =

SOLUTION:

18. f (x) = | x – 6 |

19. f (x) =

SOLUTION:

(–1, ).

f–−1

= for x ≠ −1.

20. g(x) =

SOLUTION:

(1, ).

g−1(x) =

= for x ≠ 1.

21. f (x) =

SOLUTION:

f–−1

(x) = 8 − .

, respectively.

Therefore, f−1

(x) = 8 − for x > 0.

22. g(x) =

SOLUTION:

g−1(x) = −3 +

, respectively.

Therefore, g–−1

(x) = −3 + for x > 0.

23. f (x) =

SOLUTION:

(6, ).

f–−1

for x 6.

24. h(x) =

SOLUTION:

for x ≠ .

25. g(x) = | x + 1 | + | x – 4 |

SOLUTION: a.

27. f (x) = −6x + 3

g(x) =

SOLUTION:

28. f (x) = 4x + 9

g(x) =

SOLUTION:

29. f (x) = −3x2 + 5; x ≥ 0

g(x) =

SOLUTION:

30. f (x) = + 8; x ≥ 0

g(x) =

SOLUTION:

31. f (x) = 2x3 – 6

SOLUTION:

32. f (x) =

g(x) = − 8; x ≥ 0

SOLUTION:

33. g(x) = − 4

f (x) = x2 + 8x + 8; x ≥ −4

SOLUTION:

34. g(x) = + 5

f (x) = x2 – 10x + 33; x ≥ 5

SOLUTION:

35. f (x) =

g(x) =

SOLUTION:

36. f (x) =

g(x) =

SOLUTION:

SOLUTION: a.

f −1

(x)? Explain.

f −1(x) = 10x − 1400

f −1

(x)? Explain.

SOLUTION: a.

degrees Celsius. b.

f −1 (x) = + 5

f −1 (x) = x – 11

(x) = x – 1

– 1, x ≥ –4.

59. f (x) =

Graph f .

f −1: D = x| x ≥ 0, y R, R = y | y ≥ 6, x R

60. f (x) = x2 + 9

SOLUTION:

61. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 3, x R, R = y | y 4, x R

62. f (x) =

SOLUTION: Graph f .

f −1: D = x | x 4, x R, R = y | y 3, x R

after 1984.

c(x) = 3.5x + 5(75 − x).

−1(x) represents

375, x ∈R

75 − 45 or 30.

domain of f−1

x2 is f

−1(x) = − .

domain of f−1

SOLUTION:

a. Find v

SOLUTION:

(x) = 6.25πx. v−1(1.8) ≈ 35.3.

69. [f –−1o g

−1](x)

SOLUTION:

70. [g−1o f −1

SOLUTION:

71. [f o g]−1

SOLUTION:

72. [g o f ]−1

SOLUTION:

73. (f · g)−1

SOLUTION:

must be greater than or equal to 0. Therefore, x ≥ −1.25.

74. (f −1 · g−1)(x)

SOLUTION:

Use f (x) = x2 + 1 with domain [0, ∞) and g (x) = to find each of the following.

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

Next, find the inverse.

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

81. COPIES Karen’s Copies charges users $0.40 for every minute or part of a minute to use their computer scanner. Suppose you use the scanner for x minutes, where x is any real number greater than 0. a. Sketch the graph of the function, C(x), that gives the cost of using the scanner for x minutes. b. What are the domain and range of C(x)? c. Sketch the graph of the inverse of C(x). d. What are the domain and range of the inverse? e . What real-world situation is modeled by the inverse?

SOLUTION: a. The function is C(x) = 0.4x.

b. The minutes are rounded up, so the domain will consist of whole

numbers. D=x | x R, R= y | y positive multiples of 0.4 c. To graph the inverse, interchange the axes.

d. D= x| x positive multiples of 0.4 R = y | y R e . The inverse gives the number of possible minutes spent using the scanner that costs x dollars.

82. MULTIPLE REPRESENTATIONS In this problem, you will investigate inverses of even and odd functions. a. GRAPHICAL Sketch the graphs of three different even functions. Do the graphs pass the horizontal line test? b. ANALYTICAL What pattern can you discern regarding the inverses of even functions? Confirm or deny the pattern algebraically. c. GRAPHICAL Sketch the graphs of three different odd functions. Do the graphs pass the horizontal line test? d. ANALYTICAL What pattern can you discern regarding the inverses of odd functions? Confirm or deny the pattern algebraically.

SOLUTION: a. No; sample answer:

b. Sample answer: The pattern indicates that no even functions have inverses. When a function is even, f (x) = f (−x). Two x-values share a common y-value. This violates the horizontal line test. Therefore, the statement is true, and no even functions have inverse functions. c. No; sample answer:

d. Sample answer: The pattern indicates that all odd functions have inverses. While the pattern of the three graphs presented indicates that some odd functions have inverses, this is in fact a false statement. If a

function is odd, then f (−x) = −f (x) for all x. An example of an odd

function is . Notice from the graph of this function

that, while it is odd, it fails the horizontal line test and, therefore, does not have an inverse function.

83. REASONING If f has an inverse and a zero at 6, what can you determine about the graph

of f −1?

SOLUTION:

If f has an inverse, then (x, f (x)) = (f (x), x). Therefore, f −1 has a y-intercept at (0, 6).

84. Writing in Math Explain what type of restriction on the domain is needed to determine the inverse of a quadratic function and why a restriction is needed. Provide an example.

SOLUTION: Sample answer: The domain of a quadratic function needs to be restricted so that only half of the parabola is shown. The cut-off point of the restriction will be along the axis of symmetry of the parabola. This essentially cuts the parabola into two equal halves. The restriction

will be or for f (x) = ax2 + bx + c.

85. REASONING True or False. Explain your reasoning. All linear functions have inverse functions.

SOLUTION: False; sample answer: Constant functions are linear, but they do not pass the horizontal line test. Therefore, constant functions are not one-to-one functions and do not have inverse functions.

86. CHALLENGE If f (x) = x3 − ax + 8 and f −1 (23) = 3, find the value

SOLUTION:

If f−1

(23) = 3, then (23, 3) is equal to (x, y) in f−1

Replace (x, y ) with (23, 3).

87. REASONING Can f (x) pass the horizontal line test when f (x) = 0

and f (x) = 0? Explain.

SOLUTION:

Yes; sample answer: One function that does this is f (x) = . Even

though both limits approach 0, they do it from opposite sides of 0 and nox-values ever share a corresponding y-value. Therefore, the function passes the horizontal line test.

88. REASONING Why is ± not used when finding the inverse function of

f (x) = ?

SOLUTION: Sample answer: If the ± sign is used, then f (x) will no longer be a function because it violates the vertical line test.

89. Writing in Math Explain how an inverse of f can exist. Give an example provided that the domain of f is restricted and f does not have an inverse when the domain is unrestricted.

SOLUTION:

Sample answer: If f (x) = x2, f does not have an inverse because it is not

one-to-one. If the domain is restricted to x ≥ 0, then the function is now

one-to-one and f −1 exists; f −1(x) = .

For each pair of functions, find f o g and g o f . Then state the domain of each composite function.

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

There are no restrictions on the domains.

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

Use the graph of the given parent function to describe the graphof each related function.

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

SOLUTION: a. The graph of g(x) is the graph of f (x) expanded horizontally because

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

b. This function is of the form h(x) = f (x – 5) – 2. So, the graph of h(x)is the graph of f (x) translated 5 units to the right and 2 units down. c. This function is of the form m(x) = 3f (x) + 6. So, the graph of m(x) isthe graph of f (x) expanded vertically because 3 > 1 and translated 6 units up.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

SOLUTION: a. This function is of the form g(x) = |f (x) + 3|. So, the graph of g(x) is the graph of f (x) translated 3 units up and the portion of the graph below the x-axis is reflected in the x-axis. b. This function is of the form h(x) = –f (2x). So, the graph of h(x) is the graph of f (x) compressed horizontally because 2 > 1 and reflected in the x-axis. c. This function is of the form m(x) = 0.75f (x + 1). So, the graph of m(x) is the graph of f (x) translated 1 unit to the left and compressed vertically because 0 < 0.75 < 1.

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION: a. The graph of g(x) is the graph of f (x) compressed horizontally because g(x) = |2x| = f (2x) and 2 > 1. b. This function is of the form h(x) = f (x – 5). So, the graph of h(x) is the graph of f (x) translated 5 units to the right. c. This function is of the form m(x) = f (3x) – 4. So, the graph of m(x) isthe graph of f (x) compressed horizontally because 3 > 1 and translated 4 units down.

96. ADVERTISING A newspaper surveyed companies on the annual amount of money spent on television commercials and the estimated number of people who remember seeing those commercials each week.A soft-drink manufacturer spends $40.1 million a year and estimates 78.6 million people remember the commercials. For a package-delivery service, the budget is $22.9 million for 21.9 million people. A telecommunications company reaches 88.9 million people by spending $154.9 million. Use a matrix to represent these data.

SOLUTION:

Solve each system of equations.97. x + 2y + 3z = 5

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

Subtract the 2nd equation from the first.

Subtract 2 times the 3rd

original equation from 3 times the 2nd

original equation.

Solve the new system of 2 equations. Multiply the bottom equation by 2 and add.

Substitute to find x.

Substitute into one of the original equations to find y .

Substitute all three values into the other two original equations to confirm your answer.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

Add the 1s t and 3rd equations together.

Add 2 times the 3rd original equation to the 2nd original equation.

Solve the new system of 2 equations. Solve for y in the 1s t, then

substitute into the 2nd.

Substitute for x and solve for y .

Substitute into one of the original equations to find z.

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

Add the 3rd equation to twice the 2nd equation to eliminate the y .

Solve the new system of 2 equations and 2 variables. Solve for x in

the 1s t, then substitute into the 2nd.

Substitute all three values into the last original equation to confirm youranswer.

100. BASEBALL A batter pops up the ball. Suppose the ball was 3.5 feet above the ground when he hit it straight up with an initial velocity of 80

feet per second. The function d(t) = 80t – 16t2 + 3.5 gives the ball’s

height above the ground in feet as a function of time t in seconds. How long did the catcher have to get into position to catch the ball after it was hit?

SOLUTION:

The ball will hit the ground after about 5.04 seconds, so the catcher will have about 5 seconds.

101. SAT/ACT What is the probability that the spinner will land on a number that is either even or greater than 5?

SOLUTION: The sections of the spinner are all equal and four of the 6 numbers are

either even or greater than 5. Therefore, the probability is = .

102. REVIEW If m and n are both odd natural numbers, which of the following must be true?

I. m2 + n

2 is even.

II. m2 + n

2 is divisible by 4.

III. (m + n)2 is divisible by 4.

F none G I only H I and II only J I and III only

SOLUTION:

If m is odd, then m2 equals an odd number multiplied by an odd number.

The sum of an odd number of odd numbers is always odd, so m2 will

always be odd. The same is true for n2. Since m

2 and n

2 are odd, the

sum of these two numbers will always be even. Thus, part I is true. The sum of two odd numbers is always an even number of the form 2a

where a is an integer, thus (m + n)2 = (2a)

2 = 4a

2, a ∈ Z. Since 4a

divisible by 4, Part III is true. Part II is not true when m = 1 and n = 3. Therefore, the correct choiceis J.

103. Which of the following is the inverse of f (x) = ?

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

104. REVIEW A train travels d miles in t hours and arrives at its destination3 hours late. At what average speed, in miles per hour, should the train have gone in order to have arrived on time? F t – 3

J − 3

SOLUTION:

d = rt

The train’s current rate is r = . If the train needs to arrive 3 hours

earlier, then replace t with t − 3. Therefore, r = .

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

73. (f · g)−1

SOLUTION:

74. (f −1 · g−1)(x)

SOLUTION:

75. [f −1o g

−1](x)

SOLUTION:

76. [g−1o f −1

SOLUTION:

77. [f o g]−1

SOLUTION:

78. [g o f ]−1

SOLUTION:

79. (f · g−1) (x)

SOLUTION:

80. (f −1 · g)(x)

SOLUTION:

of f −1?

SOLUTION:

If f−1

SOLUTION:

f (x) = ?

SOLUTION:

90. f (x) = x2 – 9

g(x) = x + 4

SOLUTION:

91. f (x) = x – 7

g(x) = x + 6

SOLUTION:

92. f (x) = x – 4

g(x) = 3x2

SOLUTION:

93. f (x) = x2

a. g(x) = (0.2x)2

b. h(x) = (x – 5)2 – 2

c. m(x) = 3x2 + 6

g(x) = (0.2x)2 = f (0.2x) and 0 < 0.2 < 1.

94. f (x) = x3

a. g(x) = |x3 + 3|

b. h(x) = −(2x)3

c. m(x) = 0.75(x + 1)3

95. f (x) = |x|

a. g(x) = |2x|

b. h(x) = |x – 5| c. m(x) = |3x| − 4

SOLUTION:

3x + 2y – 2z = −13

5x + 3y – z = −11

SOLUTION:

original equation.

98. 7x + 5y + z = 0

−x + 3y + 2z = 16

x – 6y – z = −18

SOLUTION:

99. x – 3z = 7 2x + y – 2z = 11

−x – 2y + 9z = 13

SOLUTION:

I. m2 + n

2 is even.

II. m2 + n

SOLUTION:

2 and n

2 are odd, the

2 = 4a

A g(x) =

B g(x) =

C g(x) = 2x + 5

D g(x) =

SOLUTION:

J − 3

SOLUTION:

d = rt

1-7 inverse relations and...

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