ujian chapter 1 add math

7/29/2019 Ujian Chapter 1 Add Math

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Diagram 1

Set BSet A

p

q

r 8

6

4

2

CHAPTER 1 FUNCTIONS FORM 4

PAPER 1

1. Diagram 1 shows the relation between set A and set B.

State

the range of the relation,

the type of the relation.

[2 marks]

2.

Based on the above information, the relation betweenR and Sis defined by the set of

ordered pairs { }),(),,(),,(),,( hbfbdaba .State

the images ofa

the object ofb

[2 marks]

1

{ }

{ }jhfdbS

cbaR

,,,,

,,

==


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g(xx

0246

-2

k0

4


3. Diagram 2 shows the linear function .g

(a) State the value of k.

(b) Using the function notation, expressgin terms ofx.

[2 marks]

2

Diagram 2


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4.Diagram 3 shows the function 0,:

+ x

x

kxxg where kis a constant.

Find the value ofk.

[2 marks]

5. Given the function 1: + xxg , find the value ofx such that 2)( =xg .[2 marks]

3

2

1

3

x

kx +x

Diagram 3


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6. Diagram 5 shows the graph of the function 62)( = xxf for domain 40 x .

State

(a) the value of t,

(b) the range off(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]

4

x4t0

6

f(x)

Diagram 5


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8. The following information is about the functiongand the composite function2g .

Find the value of a and b.

[3 marks]

9. Given the function0,

2

1)( = x

xxf and the composite function xxfg 4)( = .

Find

(a) )(xg

(b) the value ofx when 2)( =xgf

[4 marks]

5

bxaxg : , where a and b are constant and b > 089:2 + xxg


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10

. The function h is defined as3,

3

7)(

+= x

xxh .

Find

(a) )(1 xh

(b) )2(1h

[3 marks]

11

.

Diagram 9 shows the functionfmapsx toy and the functiongmapsy toz.

Determine

(a) )1(1f

(b) )5(gf

[2 marks]

6

gfzyx

4

1

5


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12

.

The following information refers to the functionfandg.

Find )(1 xgf .

[3 marks]

13. Given the function

hxxg 3: and2

1:1 kxxg , where h and kare constants. Find

the value ofh and ofk.

[3marks]

7

3:

15:

+

xxg

xxf


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14

. Given the function13)( += xxh and

3)(

xxg = . Find

(a) )7(1h

(b) )(1 xgh

[4 marks]

15

.Given the function 23: xxf and 32: 2 xxg .Find

(a) )4(1f

(b) )(xgf

[4 marks]

8


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ANSWER (PAPER 1)

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

12

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

xg4

)(2

1=

1

0,81)( = xx

xg 1

9


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(b)2

2

18

1=

x

1

8

1=x 1

10 (a)3

7=

yx

1

37

)(1 =x

xh , 0x 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

=

xxgf

1

5

4=

x

1

13.

3

hyx

+=

1

3

1=k

1

2

3=h

1

14.

(a) 3

1=

yx

1

23

17)7(1 =

=h

1

(b)

3

3

1

)(1

=x

xgh

1

9

1=x

1

15 (a)

3

2+=

yx

1

2)4(1 =f 1

(b) 3)23(2)(2 = xxgf 1

52418 2 += xx 1

10

ujian chapter 1 add math

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