1 Functions: Questions Based On SPM Format
1 Functions: Questions Based On SPM Format
1 Functions: Questions Based On SPM Format
1. 2.
P = { 1, 2}
2, 3}
Q = {2, 4, 6, 8, 10} a• •p
b• •q
Base on the information above, a relation from P into c• •r
Q is defined by the set of ordered pairs •s
{ (1, 4), (1, 6), (2, 6), (2, 8) }.
A B
State The above diagram shows the relation between set A
(a) the images of 1, Ans: and set B
(b) the object of 4, Ans: State
(c) the domain, Ans: (a) the images of b, Ans:
(d) the codomain, Ans: (b) the objects of p, Ans:
(e) the range, Ans: (c) the domain, Ans:
(f) the type of relation Ans: (d) the codomain, Ans:
(e) the range, Ans:
(f) the type of relation Ans:
3. Given the functions f : x 2 x 1 and 4. Given the functions g : x 4 x 1 and
g : x x 2 3 , find h : x x 2 3 , find
(a) f –1 (5) , (a) g –1 (3) ,
(b) gf (x) . (b) hg (x) .
Functions 1
1 3 8. Given that f : x 2 x 1 , g : x 4 x and
7. Given that f : x 4 x m and f : x nx , fg : x ax b , find the values of a and b .
4
find the values of m and n.
[ m = –3 ; n = 1
] [ a = 8 ; b = –1 ]
4
9. Given that f : x x 3 , g : x a bx 2 and 4
10. Given that g : x m 3x and g 1 : x 2kx ,
gf : x 6 x 2 36 x 56 , find the values of a and b . 3
find the values of m and k.
[a=2;b=6] 1
[k= 6 ;m=4]
2
11. Given that g(x) = mx + n and g (x) = 16x – 25 , 1 2x 3
12. Given the inverse function f ( x) , find
find the values of m and n. 2
(a) the value of f(4),
(b) the value of k if f –1 (2k) = –k – 3 .
25
[ m = 4 , n = –5 ; m = –4 , n = 3 ] [ (a) 11
; (b) k = 1
]
2 2
Functions 2
QUESTIONS BASED ON SPM FORMAT
x2 x 15 x 1 1 1
(a) 3
(b) (c) 10x – 4 (a) 2
(b) 6
x
2
(c) 18x + 9
10
3. (SPM 06, P1, Q2) p 3x
mx 4. Diagram 3 shows the function g : x ,
Diagram 2 shows the function h : x , x2
x x 2 , where p is a constant.
x 0 , where m is a constant.
g p 3x
h mx x
x x2
x
7
8
1 5
2 Diagram 3
Diagram 2
Find the value of p.
Find the value of m.
m=4 p=4
Functions 3