1. The function w is defined by f(x) = . Find

a. f –1

b. f –1 (–5)

2. Given the function , find the values of x such that f(x) = 7

3. Given that and composite function , where a and b are constants. Find the value of a and of b.

4. Given the functions and , find

a. g –1(7)b. h –1g(x)

5. Diagram show the relation between set P and set Q in the graph form. State

a. the object of bb. the relation in the form of ordered pairsc. codomain of the relationd. range of the relatione. the type of the relation

6. Given the functions and , find the value of hg(10)

(3 marks) / SPM 2010

7. 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) / SPM 2011

8. The inverse function

Finda. h(x)b. the value of x such that h(x) = –5.

(4 marks) / SPM 2011

9. Given that f(x) = 3x + 4 and fg(x) = 6x + 7, Finda. fg(4)

HIGHER ORDER THINKING SKILL (HOTS)SPM ADDITIONAL MATHEMATICS PAPER 1

HOTS DRILLING EXERCISE

Topic: Functions

Set Q

3 5 7

Set P

c

d

b

a

SPM/SBP Past-Year Questions

ReviewQuestions

b. g(x)(4 marks) / SPM 2012

1. Diagram shows the relation between set A and Set B in the arrow diagram form.

a. Represent the relation in the form of ordered pairs.b. State the domain of the relation.

(SPM 2014 / 2 marks)

2. Diagram shows the function , where m is a constant.Find the value of m.

(SPM 2014 / 2 marks)

3. Function f and g are defined by the remainder when x2 divided by 7 the remainder when x2 divided by 5

Find

i. f(5)ii g(–3)

HIGHER ORDER THINKING SKILL (HOTS)SPM ADDITIONAL MATHEMATICS PAPER 1

HOTS DRILLING EXERCISE

Topic: FunctionsHOTS (KBAT)

Questions and Answer

Set A–2 1 2

41Set B

fx

84

x – 2m

Forecast Question

s

4. Given the functions , find the function k in terms of f or/and g if

i. ii.iii.

5. Diagram shows part of the mapping y to x of function and mapping y to

z of function . Find

i. the value of p and g. ii. the function of mapping x to yiii. the function of mapping x to z

zyx

–1

–2

2

g h

6. Given the function .

i. Find f –1

ii. Determine whether f –1 is a function or not a function. Give your reason.

7. The function f is defined by where m is a constant.

a. State the value of k.b. Given that the value of 1 is unchanged under this mapping, find

i. the value of m.ii. the other value of x which is unchanged.

8. Diagram shows the function f and g. Given the function f is defined by

.

Finda. the function g in similar form.b. g(4)

9. Diagram shows the function f, g and h. Given that the function f is defined by and the function g is defined by

Finda. the function h in similar form.b. h(–2)

f

g

yx

f g

yx z

h

10. Diagram shows the graph of function y = f(x). In the answer space provided, sketch the graph

of f –1

Answer;

11. Diagram shows the graph of function . In the answer space provided, sketch the graph

of f –1

Answer;

12. Diagram shows the graph of function . In the answer space provided, sketch the graph

of f –1

Answer;

f(x)

x

0

(–2, 2)

(2, 2)

f(x)

x

xx:f

0

f(x)

x

0

f(x)

x

(2, 4)

0

f(x)

x

f(x) = x2

f(x)

x

13. A function f defined by . Find the function g if

a.b.c.

14. M = {4, 6, 8, 10} and N = {2, 3, 4}

Based on the above information, the relation between M and N is defined by the set of ordered

pairs;

{ (4, 2), (4, 4), (6, 2), (6, 3). (8, 2), (8, 4), (10, 2) }. State

a. the images of 4b. the object of 3c. the type of relation.

15. By using the same axes, sketch the graph of f –1 , for each of the following diagrams. Hence,

a. State the domain of f –1 .b. Find the value(s) of x, (If it exists), for which f(x) = f –1(x)

i. Answer;

ii. Answer;

(0, 4)

y

x0 (8, 0)

f

(1, 1)

y

x0

(2, 8)

f

(–1, –1)

(1, 1)

y

x0

(2, 8)

f

(–1, –1)

(0, 4)

y

x0 (8, 0)

f

iii. Answer;

16. Diagram shows the relation between set P and Set Q in the arrow diagram form.State

a. the type of relation.b. the range of the relation.

(1, 8)

y

x0

(8, 1)

f

(2, 4)

Set Q–2 1 2

41Set P

(1, 8)

y

x0

(8, 1)

f

(2, 4)