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1. CHAPTER 1
FUNCTIONS
FORM 4
PAPER 1
1.
Diagram 1 shows the relation between set A and set B.
2
p
4
6
8
q
r
Set A
Set B
Diagram 1
State
(a) the range of the relation,
(b) the type of the relation.
[2 marks]
2.
3.
R = {a, b, c}
S = {b, d , f , h, j}
Based on the above information, the relation between R and S is defined by the set of
ordered pairs {( a, b), ( a, d ), (b, f ), (b, h)} .
State
(a) the images of a
(b) the object of b
[2 marks]
Diagram 2 shows the linear function g .
x
g(x)
0
2
4
6
-2
0
k
4
Diagram 2
(a) State the value of k.
(b) Using the function notation, express g in terms of x.
[2 marks]
4.
Diagram 3 shows the function g : x →
x
x+k
, x ≠ 0 where k is a constant.
x
x +k
x
3
1
2
Diagram 3
Find the value of k.
1

2. CHAPTER 1
5.
Given the function
FUNCTIONS
g : x →x +1 ,
FORM 4
find the value of x such that g ( x) = 2 .
[2 marks]
[2 marks]
6.
Diagram 5 shows the graph of the function
f ( x ) = 2 x −6
for domain 0 ≤ x ≤ 4 .
f(x)
6
t
0
4
x
Diagram 5
State
(a) the value of t,
(b) the range of f(x) corresponding to the given domain.
[3 marks]
7.
Given the function f ( x) = 2 x +1 and g ( x) = 3 − kx , find
(a) f (2)
(b) the value of k such that gf ( 2) = −7
[3 marks]
8.
The following information is about the function g and the composite function g 2 .
g : x → a − bx ,
where a and b are constant and b > 0
g 2 : x → 9x + 8
Find the value of a and b.
[3 marks]
9.
Given the function f ( x) =
1
,
2x
x ≠ 0 and the composite function fg ( x) = 4 x .
Find
(a) g ( x)
(b) the value of x when gf ( x) = 2
[4 marks]
10
.
The function h is defined as h( x) =
Find
(a) h −1 ( x)
(b) h −1 ( 2)
7
,
3+ x
x ≠ −3 .
[3 marks]
2

3. CHAPTER 1
11
.
FUNCTIONS
FORM 4
Diagram 9 shows the function f maps x to y and the function g maps y to z.
x
f
y
g
z
5
4
1
Determine
(a) f −1 (1)
(b) gf (5)
[2 marks]
12
.
The following information refers to the function f and g.
f : x → 5 x +1
g : x → x −3
Find f
−
1
g ( x) .
[3 marks]
13
.
1
2
−1
Given the function g : x →3 x − h and g : x → kx − , where h and k are constants. Find
the value of h and of k.
[3marks]
14
.
Given the function h( x ) = 3x +1 and g ( x ) =
x
. Find
3
(a) h −1 (7)
(b) gh −1 ( x )
[4 marks]
15
.
Given the function f : x → 3 x − 2 and g : x → 2 x 2 − 3 .
Find
(a) f −1 ( 4)
(b) gf (x )
[4 marks]
ANSWER (PAPER 1)
3

4. CHAPTER 1
FUNCTIONS
FORM 4
2 (a)
(b)
3 (a)
(b)
4
1
many-to-one
1
b , d
1
a
1
k =2
1
g ( x) = x − 2
1
1
k =1
(b)
{4, 8}
1
+k
1 2
g  =
=3
1
2
2
1 (a)
1
x +1 = 2
5
or − ( x +1) = 2
x =1
6 (a)
x = −3
When f ( x ) = 0 , 2 x − 6 = 0
1
1
1
x =3
∴ t =3
(b)
Range :
7 (a)
f ( 2) = 5
(a)
(b)
0 ≤ f ( x) ≤ 6
(b)
1
1
g (5) = −7
3 − k (5) = −7
1
k =2
1
g 2 ( x ) = a − b( a − bx)
8
1
1
= a − ab + b 2 x
b2 = 9
and
a − ab = 8
b =3
9 (a)
(b)
1
= 4x
2 g ( x)
1
g ( x) =
,
8x
1
=2
1 
8 x 
2 
a = −4
1
1
1
x≠0
1
1
4

5. CHAPTER 1
FUNCTIONS
x=
10 (a)
x=
1
8
FORM 4
1
1
7
−3
y
7
−3 , x ≠ 0
x
1
h −1 ( 2) =
2
1
11 (a)
5
1
(b)
4
1
h −1 ( x) =
(b)
12
x=
14.
(a)
(b)
15 (a)
−1
f
(b)
1
( x − 3) −1
5
x −4
=
5
y +h
x=
3
1
k=
3
3
h =−
2
y −1
x=
3
7 −1
h −1 (7) =
=2
3
x −1
gh −1 ( x) = 3
3
x −1
=
9
y+2
x=
3
f
13.
y −1
5
g ( x) =
−1
1
( 4) = 2
1
1
1
1
1
1
1
1
1
1
1
gf ( x) = 2(3 x − 2) 2 − 3
= 18 x − 24 x + 5
2
1
1
5

6. CHAPTER 1
FUNCTIONS
x=
10 (a)
x=
1
8
FORM 4
1
1
7
−3
y
7
−3 , x ≠ 0
x
1
h −1 ( 2) =
2
1
11 (a)
5
1
(b)
4
1
h −1 ( x) =
(b)
12
x=
14.
(a)
(b)
15 (a)
−1
f
(b)
1
( x − 3) −1
5
x −4
=
5
y +h
x=
3
1
k=
3
3
h =−
2
y −1
x=
3
7 −1
h −1 (7) =
=2
3
x −1
gh −1 ( x) = 3
3
x −1
=
9
y+2
x=
3
f
13.
y −1
5
g ( x) =
−1
1
( 4) = 2
1
1
1
1
1
1
1
1
1
1
1
gf ( x) = 2(3 x − 2) 2 − 3
= 18 x − 24 x + 5
2
1
1
5