Cambridge Additional Mathematics

46 Functions (Chapter 2)

Themodulusorabsolute valueof a real number is its size, ignoring

its sign.

We denote the absolute value ofxbyjxj.

For example, the modulus of 4 is 4 , and the modulus of¡ 9 is 9 .We

write j 4 j=4and j¡ 9 j=9.

Example 7 Self Tutor

If x=¡ 3 , find the value of:

a jxj b xjxj c

̄

̄x^2 +x

̄

̄ d

̄

̄

̄

7 x¡ 1

2

̄

̄

̄

a jxj

=j¡ 3 j

=3

b xjxj

=(¡3)j¡ 3 j

=¡ 3 £ 3

=¡ 9

c

̄

̄x^2 +x

̄

̄

=

̄

̄(¡3)^2 +(¡3)

̄

̄

=j 6 j

=6

d

̄

̄

̄

7 x¡ 1

2

̄

̄

̄

=

̄

̄

̄

7(¡3)¡ 1

2

̄

̄

̄

=j¡ 11 j

=11

EXERCISE 2D.1

1 Find the value of:

a j 5 j b j¡ 5 j c j 7 ¡ 3 j d j 3 ¡ 7 j

e

̄

̄ 22 ¡ 10

̄

̄ f j 15 ¡ 3 £ 5 j g

̄

̄

̄

3 ¡ 1

5+2

̄

̄

̄ h

̄

̄

̄

̄

23

(¡3)^3

̄

̄

̄

̄

2 If x=4, find the value of:

a jx¡ 5 j b j 10 ¡xj c

̄

̄ 3 x¡x^2

̄

̄ d

̄

̄

̄

2 x+1

x¡ 1

̄

̄

̄

3 If x=¡ 2 , find the value of:

a jxj b xjxj c ¡

̄

̄x¡x^2

̄

̄ d j1+3xj

x+1

MODULUS EQUATIONS

The equation jxj=2 has two solutions: x=2and x=¡ 2.

If jxj=a where a> 0 , then x=§a.

If jxj=jbj then x=§b.

We use these rules to solve equations involving the modulus function.

D The modulus function

The absolute value of a

number is always> 0.

Solving modulus equations

is not needed for the syllabus.

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_02\046CamAdd_02.cdr Tuesday, 8 April 2014 10:25:17 AM BRIAN