The document contains a mathematics exam with 15 multiple-choice questions related to functions. It includes diagrams of various functions and asks students to identify properties of the functions such as their domain and range, determine function values, and perform operations on composite functions.

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

2. CHAPTER 1 FUNCTIONS FORM 4
[2 marks]
5. Given the function 1: +→xxg , find the value of x such that 2)( =xg .
[2 marks]
6. Diagram 5 shows the graph of the function 62)( −= xxf for domain 40 ≤≤ x .
State
(a) the value of t,
(b) the range of f(x) corresponding to the given domain.
[3 marks]
7. Given the function 12)( += xxf and kxxg −= 3)( , find
(a) )2(f
(b) the value of k such that 7)2( −=gf
[3 marks]
8. The following information is about the function g and the composite function 2
g .
Find the value of a and b.
[3 marks]
9.
Given the function 0,
2
1
)( ≠= x
x
xf and the composite function xxfg 4)( = .
Find
(a) )(xg
(b) the value of x when 2)( =xgf
[4 marks]
10
.
The function h is defined as 3,
3
7
)( −≠
+
= x
x
xh .
Find
(a) )(1
xh−
(b) )2(1−
h
[3 marks]
2
x
4t0
6
f(x)
Diagram 5
bxaxg −→: , where a and b are constant and b > 0
89:2
+→ xxg

3. CHAPTER 1 FUNCTIONS FORM 4
11
.
Diagram 9 shows the function f maps x to y and the function g maps y to z.
Determine
(a) )1(1−
f
(b) )5(gf
[2 marks]
12
.
The following information refers to the function f and g.
Find )(1
xgf −
.
[3 marks]
13
.
Given the function hxxg −→3: and
2
1
:1
−→−
kxxg , where h and k are constants. Find
the value of h and of k.
[3marks]
14
.
Given the function 13)( += xxh and
3
)(
x
xg = . Find
(a) )7(1−
h
(b) )(1
xgh−
[4 marks]
15
.
Given the function 23: −→ xxf and 32: 2
−→ xxg .
Find
(a) )4(1−
f
(b) )(xgf
[4 marks]
ANSWER (PAPER 1)
3
gf
zyx
4
1
5
3:
15:
−→
+→
xxg
xxf

4. CHAPTER 1 FUNCTIONS FORM 4
1 (a) { }8,4 1
(b) many-to-one 1
2 (a) b , d 1
(b) a 1
3 (a) 2=k 1
(b) 2)( −= xxg 1
4
3
2
1
2
1
2
1
=
+
=





k
g
1
1=k 1
5 21 =+x or 2)1( =+− x 1
1=x 3−=x 1
6 (a) When 0)( =xf , 062 =−x 1
3=x
3=∴ t 1
(b) Range : 6)(0 ≤≤ xf 1
7 (a) (a) 5)2( =f 1
(b) (b) 7)5( −=g
7)5(3 −=−k 1
2=k 1
8 )()(2
bxabaxg −−= 1
xbaba 2
+−=
92
=b and 8=− aba 1
3=b 4−=a 1
9 (a)
x
xg
4
)(2
1
=
1
0,
8
1
)( ≠= x
x
xg
1
(b)
2
2
1
8
1
=






x
1
4

5. CHAPTER 1 FUNCTIONS FORM 4
8
1
=x 1
10 (a) 3
7
−=
y
x 1
3
7
)(1
−=−
x
xh , 0≠x
1
(b)
2
1
)2(1
=−
h
1
11 (a) 5 1
(b) 4 1
12
5
1−
=
y
x
1
5
1)3(
)(1 −−
=− x
xgf
1
5
4−
=
x 1
13.
3
hy
x
+
=
1
3
1
=k
1
2
3
−=h
1
14.
(a) 3
1−
=
y
x
1
2
3
17
)7(1
=
−
=−
h
1
(b)
3
3
1
)(1
−
=−
x
xgh
1
9
1−
=
x 1
15 (a)
3
2+
=
y
x
1
2)4(1
=−
f 1
(b) 3)23(2)( 2
−−= xxgf 1
52418 2
+−= xx
1
5

6. CHAPTER 1 FUNCTIONS FORM 4
8
1
=x 1
10 (a) 3
7
−=
y
x 1
3
7
)(1
−=−
x
xh , 0≠x
1
(b)
2
1
)2(1
=−
h
1
11 (a) 5 1
(b) 4 1
12
5
1−
=
y
x
1
5
1)3(
)(1 −−
=− x
xgf
1
5
4−
=
x 1
13.
3
hy
x
+
=
1
3
1
=k
1
2
3
−=h
1
14.
(a) 3
1−
=
y
x
1
2
3
17
)7(1
=
−
=−
h
1
(b)
3
3
1
)(1
−
=−
x
xgh
1
9
1−
=
x 1
15 (a)
3
2+
=
y
x
1
2)4(1
=−
f 1
(b) 3)23(2)( 2
−−= xxgf 1
52418 2
+−= xx
1
5