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DESCRIPTION
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FUNCTIONS
PAPER 1
1. Based on the above information , the relation between P and Q is defined by the set of ordered pairs {(1, 2), (1, 4), (2, 6), (2, 8)}. State(a) the image of object 1,(b) the object of 6. [2 marks]
Answer : (a) …………………………...
(b) …………………………..2. Given and , find
(a) g -1 (3),
(b) hg(x) [4 marks]
Answer : (a) …………………………...
(b) …………………………..
1
P = {1, 2, 3} Q = {2, 4, 6, 8, 10}
3. Diagram 1 shows the relation of P to Q.
d w
e x
f y
z
DIAGRAM 1
State(a) The range of the relation,(b) The type of the relation. [2 marks]
Answer : (a) …………………………...
b) …………………………..
4. Given function and , where m and k are constants find
the value of m and k. [4 marks]
Answer : …………………………...
2
5. Given the function and the composite function ,find
(a)
(b) The value of x when [4 marks]
Answer : (a) …………………………...
(b) …………………………..
6. Diagram 2 shows that function h maps x onto y and function g maps y onto z.
DIAGRAM 2
Calculate
(a) h -1(5),
(b) gh(2). [2 marks]
Answer : (a) …………………………...
(b) …………………………..
3
x y zh g
2
5
8
7. A function is defined as , x 2.
Find
(a) w -1(x),
(b) w -1(4). [4 marks]
Answer : (a) …………………………...
(b) …………………………..
8. The information below defines the functions h and g.
Find gh -1(x). [4
marks]
Answer: ………………………….......
4
h : x 2x – 3
g : x 4x – 1
9. In diagram 3, set B shows the images of certain elements of set A.
(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.
[3 marks]
Answer : (a) …………………………...
(b) …………………………..
5
25
16
5 ● 4 ●
-4 ●
-5 ●
>
> >>
Set A
Set B
DIAGRAM 3
10. Diagram 4 shows the function ,where m is a constant.
Find the value of m. [2marks]
Answer : ………………………….......
11. Given f (x) = 4 – 3x and fg(x) = 10 – 5x. Find the function g. [3 marks]
Answer : ………………………….......
8
m xx-
x
6
DIAGRAM 4
12. Given g : x px + q, p 0 and g2 : x 4x – 15. Find the value of p and q. [4 marks]
Answer : ………………………….......
13. Given f : x 4x – 1 and g : x x2 + 3,find
(a) fg(-3),
(b) the value of x when f 2(x) = 7. [4 marks]
Answer : (a) …………………………...
(b) …………………………..
PAPER 2
1. Given and , find
(a) [1marks]
(b) [2marks]
(c) such that [3marks]
ANSWER
7
PAPER 1
1. (a) 2, 4
(b) 2
2. (a)
(b)
3. (a) range = { x , y }
(b) many-to-one relation
4.
5. (a)
(b) x = 15
6. (a)
(b)
7. (a)
(b)
8. 2x + 5
9. (a) many-to-one relation
(b)
10. 4
11.
12. p = 2, q = -5
13. (a) 47
(b)
PAPER 2
1. (a)
(b)
(c)
8