1.In Diagram below, the function h maps x to y and the function g maps y to z.

Diagram

Determine(a) h–1(5). Ans:2 (b) gh(2). Ans:8

[2 marks]2.The function w is defined as

. Find (a) w–1(x). Ans: 2x-5 (b) w–1(4). Ans: 3/4 x

[3 marks]

3.The following information refers to the functions h and g.

Ans: 2x + 5 Find gh–1(x).

[3 marks]4.In Diagram below, set B shows the images of certain elements of set A.

Diagram (a)State the type of relation between set A and set B.

(b) Using the function notation, write a relation between set A and set B. Ans: f : x → x2

[2 marks]

5.Diagram below shows the function , where m is a constant.

                   Diagram Find the value of m. Ans: m = 4

[2 marks]

6.Diagram below shows the linear function h.

Diagram

(a) State the value of m    Ans:m = 3 (b) Using the function notation, express h in terms of x. Ans:h : x → x + 1

[2 marks]7. Given the function f : x → |x – 3|, find the values of x such that f (x) = 5. Ans:x = –2 or 8

[2 marks]8.The following information is about the function h and the composite function h2.

Ans: a = 6 and b = –5 Find the value of a and of b.

[3 marks]9.Diagram below shows the graph of the function f (x) = |2x – 1|, for the domain 0 ≤ x ≤ 5.

Diagram State (a)the value of t. Ans: t=1/2 (b) the range of f (x) corresponding to the given domain Ans:0 ≤ f (x) ≤ 9

10.Given the functions g : x → 5x + 2 and h : x → x2 – 4x + 3, find (a) g–1(6). Ans:4/5 (b) hg(x). Ans: 25x

2 – 1

11. Given the functions f (x) = x – 1 and g(x) = kx + 2, find      (a) f (5) Ans: 4 (b) the value of k such that gf (5) = 14. Ans: 3

12. Diagram below shows the relation between set X and set Y in the graph form

Diagram State (a) the objects of q. Ans: 2 and 6 (b) the codomain of the relation. Ans: {p, q, r, s}

13. Given the functions g : x → 2x – 3 and h : x → 4x, find

      (a) hg(x) Ans:8x-12 (b) the value of x if hg(x) = g(x). Ans:3/2

14.Given the function g : x → 3x – 1, find (a) g(2) Ans: 5 (b) the value of p when g–1(p) = 11. Ans:32

15.Diagram below shows the relation between set X and set Y in the graph form.

Diagram State

(a) the relation in the form of ordered pairs. (b)the type of the relation. (c)the range of the relation.

16. Given the functions g : x → 2x + 1 and h : x → 3x + 6, find (a) g–1(x). Ans: x-1 (b) hg–1(9). Ans:18 2

17. Given the functions g : x → x – 8 and , find the value of hg(10). Ans:1/2

18. It is given that the relation between set X = {0, 1, 4, 9, 16} and set Y = {0, 1, 2, 3, 4, 5, 6} is ‘square of’. (a) Find the image of 9. (b) Express the relation in the form of ordered pairs.

19. It is given that the functions g(x) = 4x – 7 and h(x) = 2x. Find the value of gh(2). Ans :9

20. The inverse function h–1 is defined by Find (a) h(x). Ans: 3x-2 (b) the value of x such that h(x) = –5. Ans X= 1/4 x

21. Diagram shows the relation between set M and set N.

Diagram State (a)the object of –1. (b) the range of the relation

22. Given that f (x) = 3x + 4 and fg(x) = 6x + 7, find (a)fg(4) Ans:31 (b)g(x) Ans: 2x + 1

23. Given that f : x → x + 5, find (a) f(3) Ans:8 (b)the value of k such that 2f –1(k) = f (3). Ans:9

24. Diagram below shows the relation between set P and set Q in the graph form. State

(a)the range of the relation (b ) the type of relation between set P and set Q [2 marks]

25. Given the function and , find gf(x). [2 marks]

26.It is given that the function , where p is a constant. Find the value of p such that f(p) = 4. [2 marks]

27. Diagram below shows the relation between set A and set B in the arrow diagram form.

(a) represent the relation in the form of ordered pairs (b)state the domain of the relation [2 marks]

28. Diagram below shows the function , where m is constant

Find the value of m. [2 marks]