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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


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