![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}](https://image.slidesharecdn.com/1-170106132643/85/1-funtions-1-1-320.jpg)
![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](https://image.slidesharecdn.com/1-170106132643/85/1-funtions-1-2-320.jpg)
![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](https://image.slidesharecdn.com/1-170106132643/85/1-funtions-1-3-320.jpg)
![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](https://image.slidesharecdn.com/1-170106132643/85/1-funtions-1-4-320.jpg)
![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](https://image.slidesharecdn.com/1-170106132643/85/1-funtions-1-5-320.jpg)
![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](https://image.slidesharecdn.com/1-170106132643/85/1-funtions-1-6-320.jpg)
![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](https://image.slidesharecdn.com/1-170106132643/85/1-funtions-1-7-320.jpg)
1.funtions (1)
- 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