FUNCTIONS
PAPER 1
P = {1, 2, 3}
Q = {2, 4, 6, 8, 10}
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 g : x  5 x  1 and h : x  x  2 x  3 , find
2
(a)
g 1 (3),
(b)
hg(x)
[4 marks]
Answer : (a) …………………………...
(b) …………………………..
1
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 h : x  4x  m and h 1 : x  2kx 
find the value of m and k.
5
, where m and k are constants
8
[4 marks]
Answer : …………………………...
2
5.
Given the function h( x ) 
6
, x  0 and the composite function hg ( x)  3x , find
x
(a) g ( x )
(b) The value of x when gh( x)  5
[4 marks]
Answer : (a) …………………………...
(b) …………………………..
6.
Diagram 2 shows that function h maps x onto y and function g maps y onto z.
h
x
g
y
z
8
5
2
DIAGRAM 2
Calculate
(a)
h 1(5),
(b)
gh(2).
[2 marks]
Answer : (a) …………………………...
(b) …………………………..
3
7.
A function is defined as w( x) 
5
, x  2.
2 x
Find
(a)
w 1(x),
(b)
w 1(4).
[4 marks]
Answer : (a) …………………………...
(b) …………………………..
8.
The information below defines the functions h and g.
h : x  2x – 3
g : x  4x – 1
Find gh -1(x).
[4 marks]
Answer: ………………………….......
4
9.
In diagram 3, set B shows the images of certain elements of set A.
5●
4●
-4 ●
>
>
>
>

25

16
-5 ●
Set B
Set A
DIAGRAM 3
(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
10.
Diagram 4 shows the function h : x 
m x
, x  0 ,where m is a constant.
x
mx
x
x
8

1
2
DIAGRAM 4
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 : ………………………….......
6
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 f : x  3x  2 and g : x 
x
 1 , find
5
(a)
f 1 ( x)
[1marks]
(b)
f 1 g ( x)
[2marks]
(c)
h( x) such that hg ( x)  2 x  6
[3marks]
7
ANSWERS - FUNCTIONS
PAPER 1
1.
2.
3.
PAPER 2
(a)
2, 4
(b)
2
(a)
f 1 
2
5
(b)
f g ( x) 
(b)
hg ( x)  25x 2  2
(c)
h  x   10 x  4
(a)
range = { x , y }
(b)
many-to-one relation
4.
1
5
k  ,m  
8
2
5.
(a)
g ( x) 
(b)
x = 15
(a)
h1 (5)  2
(b)
gh(2)  8
(a)
w 1 ( x) 
2x  5
x
(b)
w 1 ( 4) 
3
4
6.
7.
x2
3
(a)
1.
x  15
15
2
,x  0
x
8.
2x + 5
9.
(a) many-to-one relation
(b)
1
f ( x)  x 2
10.
4
11.
g ( x) 
12.
p = 2, q = -5
13.
(a)
47
(b)
3
4
5x  6
3
8