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 − 2 x + 3 , find (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 → 4 x + m and h −1 : x → 2kx + the value of m and k.
5 , where m and k are constants find 8
[4 marks]
Answer : …………………………...
2
5.
6 Given the function h( x) = , x ≠ 0 and the composite function hg ( x) = 3 x ,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. x
h
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) = Find (a)
w −1(x),
(b)
w −1(4).
5 , x ≠ 2. 2−x
[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 ●
> >
> >
-5 ●
•
25
•
16
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
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 → 3 x − 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
ANSWER PAPER 2 PAPER 1 1.
2.
3.
1.
x+2 3
2, 4
(b)
2
(b)
f g ( x) =
(a)
2 5
(c)
h ( x ) = 10 x − 4
(b)
hg ( x) = 25 x 2 + 2
(a)
range = { x , y }
(b)
many-to-one relation
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
7.
f −1 =
(a)
4.
6.
(a)
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