1)given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)explain, in words...

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1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing for all x, then f has an inverse. 3)Why does y = x 2 not really have an inverse?

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Page 1: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing

1) Given f(x) = x5 + 8x3 + x + 1 has an inverse, find f-1(1) and f-1(11).

2) Explain, in words and a picture, why this is true: if f(x) is increasing for all x, then f has an inverse.

3) Why does y = x2 not really have an inverse?

Page 2: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing

Unit Circle1) Draw a large circle, centered at the origin.2) Label the coordinates of the circle at the axes.3) Draw in radii at every 45° measure then label all

the radians for these degrees.4) Draw in radii at every 30° measure then label all

the radians for these degrees.5) Draw on your paper an equilateral and isosceles

right triangles.6) See if you can remember the rules on these

special triangles.

Page 3: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing

Page 4: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing

Page 5: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing

Page 6: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing

Page 7: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing

Page 8: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing

Page 9: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing

Page 10: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing

Page 11: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing

Page 12: 1)Given f(x) = x 5 + 8x 3 + x + 1 has an inverse, find f -1 (1) and f -1 (11). 2)Explain, in words and a picture, why this is true: if f(x) is increasing

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