f4c1 functions

8/11/2019 F4C1 Functions

1/12

SPM QUESTIONS FORM 4 CHAPTER 1 FUNCTIONS

Chapter 1 Functions Page 1

PAPER 1

10}8,6,4,2,{

3}2,1,{

Q

P

YEAR 2003

1.

Based on the above information, the relation betweenPand Qis defined by the set of ordered pairs {(1, 2), (1,4), (2, 6), (2, 8)}State

(a)

the image of 1,

(b)

the object of 2.

[2 marks

2. Given that 15: xxg and 32: 2 xxxh , find

(a) )3(1g ,

(b) )(xhg .

[4 marks

YEAR 2004

3.

Diagram 1 shows the relation between setPand set Q.

SetP Set Q

Diagram 1

State

(a)

the range of the relation,

(b)

the type of the relation.

[2 marks

4. Given the functions8

52:and4: 1 kxxhmxxh , where mand kare constants, find the values of mand k.

[3 marks

d

e

f

w

x

y

z


2/12



5.

Given the function 0,6

)( xx

xh and the composite function xxhg 3)( , find

(a) )(xg

(b) the value ofxwhen 5)( xgh .[4 marks

YEAR 2005

6.

In Diagram 2, the function h mapsxtoyand the functiongmapsytoz.

h g

x y z

Diagram 2

Determine

(a)

)5(1h ,

(b)

)2(gh .

[2 marks

7. The function wis defined as 2,

2

5)(

x

x

xw .

(a)

)(1 xw ,

(b)

)4(1

w .

[3 marks

8.

The following information refers to the functions handg.

14:

32:

xxg

xxh

Find )(1 xgh .

[3 marks

8

2

5


3/12



YEAR 2006

9. In Diagram 1, setBshows the images of certain elements of setA.

SetA

Set A Set B

Diagram 1

(a) State the type of relation between setAand setB.

(b)

Using the function notation, write a relation between set Aand setB.

[2 marks

10.

Diagram 4 shows the function ,0,:

xx

xmxh where mis a constant.

xx

xm

8

2

1

Diagram 4

Find the value of m. [2 marks]

YEAR 2007

11. Diagram 1 shows the linear functions h.

Diagram 1

(a) State the value of m.(b) Using the function notation, express hin terms ofx. [2 marks ]

5

4

-4

-5

25

16

h


4/12



.

12. Given the function 3: xxf , find the values of xsuch that 5)( xf .

[2 marks]

13. The following information is about the function h and the composite function2h .

Find the value of aand of b.

[3 marks]

YEAR 2008

14.

Diagram 1 shows the graph of function 12)( xxf , for the domain 50 x .

Diagram 1

State

(a)

the value of t,

(b)

the range of )(xf corresponding to the given domain.[3 marks]

15. Given the functions 25: xxg and 34: 2 xxxh , find

(a) )6(1g ,

(b) )(xhg

[4 marks]

baxxh : , where aand bare constants, and a>0

3536:2 xxh


5/12



16.

Given the functions 1)( xxf and 2)( kxxg , find

(a) )5(f ,

(b) the value of ksuch that 14)5( gf .

[3 marks]

YEAR 2009

17.

Diagram 1 shows the relation between set X and set Y in the graph form.

Diagram 1

State

(a)

the objects of q.

(b) the codomain of the relation.

[2 marks]

18.

Given the functions 32: xxg and xxh 4: , find

(a)

)(xhg ,

(b) the value of x if )(2

1)( xgxhg .

[4 marks]

19.

Given the function 13: xxg , find

(a)

)2(g ,

(b)

the value of p when 11)(1

pg .

[3 marks]


6/12



YEAR 2010

20. Diagram 1 shows the relation between set X and set Y in the graph form.

Diagram 1State

(a)

the relation in the form of ordered pairs.

(b)

the type of the relation.

(c)

the range of the relation.

[3 marks]

21.

Given the functions 12: xxg and 63: xxh , find

(a)

)(1 xg .

(b)

)9(1hg .

[3 marks]

22. Given the functions 8: xxg and3

2,

23:

x

x

xxh , find the value of )10(hg .

[3 marks]


7/12



YEAR 2011

23. It is given that the relation between Set X ={0, 1, 4,9, 16} and set Y = {0, 1, 2, 3, 4, 5, 6 } is square of

(a) Find the image of 9.

(b) Express the relation in the form of ordered pairs.

[ 3 marks]

24.

It is given that the function 74)( xxg and xxh 2)(

Find the value ofgh(2).

[ 2 marks ]

25.

The inverse function1h is defined by 3,

3

2:1

xx

xh ,

Find

(a) h(x)

(b) the value of x such that h(x) = -5

[ 4 marks ]

YEAR 2012

26.

Diagram 1 shows the relation between the set M and set N.

State

(a)

the object of -1,

(b)

the range of the relation.

[2 marks


8/12



27. Given thatf(x)=3x+4andfg(x)=6x+7, find

(a) fg(4)

(b) g(x)

[ 4 marks

28.

Given that 5: xxf , find

(a)

f(3)

(b)

the value of k such that )3()(2 1 fkf

[3 marks

PAPER 2

YEAR 2006

1. Given that 23: xxf and 15

: x

xg , find

(a)

)(1

xf

, [1 marks

(b) )(1 xgf , [2 marks

(c) )(xh such that 62)( xxgh . [3 marks


9/12



ANSWERS (FUNCTION)

PAPER 1

1.

(a) 2 or 4

(b) 1

2.

1 2( ) (3)5

a g

(a)

)(xhg = 25x2+ 2

3.

(a)

range = {x,y}

(b)

many to one relation.

4.

1 5

8 2k m

5.

2(a) ( ) , 0g x x

x

(b) 15x .

6.

(a) 2)5(1

h


10/12



(b)

(2) 8gh

7.

1 2 5(a) ( ) , x 0x

w xx

1 3(b) (4)4

w

8. 1( ) 2 5gh x x

9.

(a) Many to one relation

(b)

2: xxf

10. 4m


11/12




12/12



PAPER 2

1.

1 2

(a) ( ) 3

x

f x

1 5(b) ( )15

xf g x

(c) ( ) 10 4h x x

f4c1 functions

Documents