The document contains 13 math problems involving functions. The problems cover topics such as: - Finding the image and object of elements under a given function - Finding inverse functions - Determining the type of relation between sets - Evaluating composite functions - Solving for unknown constants in function definitions - Finding the value of x when a composite function equals a given value The document provides the problems and blank spaces for the answers. The answers section gives the solutions to each of the 13 problems.

1. 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 15: +→ xxg and 32: 2
+−→ xxxh , find
(a) g −1
(3),
(b) hg(x) [4 marks]
Answer : (a) …………………………...
(b) …………………………..
1
P = {1, 2, 3}
Q = {2, 4, 6, 8, 10}

2. 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 mxxh +→ 4: and
8
5
2:1
+→−
kxxh , where m and k are constants find
the value of m and k. [4 marks]
Answer : …………………………...
2

3. 5. Given the function
6
( ) , 0h x x
x
= ≠ and the composite function ( ) 3hg x x= , find
(a) ( )g x
(b) The value of x when ( ) 5gh x = [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 z
h g
2
5
8

4. 7. A function is defined as
x
xw
−
=
2
5
)( , 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

5. 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

6. 10. Diagram 4 shows the function : , 0
m x
h x x
x
−
→ ≠ ,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 x
x
−x
6
DIAGRAM 4

7. 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 : 3 2f x x→ − and : 1
5
x
g x → + , find
(a) 1
( )f x−
[1marks]
(b) 1
( )f g x−
[2marks]
(c) ( )h x such that ( ) 2 6hg x x= + [3marks]
7

8. ANSWERS - FUNCTIONS
PAPER 1
1. (a) 2, 4
(b) 2
2. (a)
2
5
(b) 2
( ) 25 2hg x x= +
3. (a) range = { x , y }
(b) many-to-one relation
4.
1 5
,
8 2
k m= = −
5. (a)
2
( ) , 0g x x
x
= ≠
(b) x = 15
6. (a) 1
(5) 2h−
=
(b) (2) 8gh =
7. (a)
x
x
xw
52
)(1 −
=−
(b)
4
3
)4(1
=−
w
8. 2x + 5
9. (a) many-to-one relation
(b) 2
( )f x x=
10. 4
11.
5 6
( )
3
x
g x
−
=
12. p = 2, q = -5
13. (a) 47
(b)
3
4
PAPER 2
1. (a)
1 2
3
x
f − +
=
(b)
1 15
( )
15
x
f g x
− +
=
(c) ( ) 10 4h x x= −
8