Cambridge Additional Mathematics

Functions (Chapter 2) 45

Example 6 Self Tutor

State the domain and range of each of the following functions:

a f(x)=

p

x¡ 5 b f(x)=

1

x¡ 5

c f(x)=

1

p

x¡ 5

a

b

c

2 State the values ofxfor whichf(x)is defined, and hence state the domain of the function.

a f(x)=

p

x+6 b f:x 7!

1

x^2

c f(x)=

¡ 7

p

3 ¡ 2 x

3 Find the domain and range of each of the following functions:

a f:x 7! 2 x¡ 1 b f(x)=3 c f:x 7!

p

x

d f(x)=

1

x+1

e f(x)=¡

1

p

x

f f:x 7!

1

3 ¡x

4 Use technology to help sketch graphs of the following functions. Find the domain and range of each.

a f(x)=

p

x¡ 2 b f:x 7!

1

x^2

c f:x 7!

p

4 ¡x

d y=x^2 ¡ 7 x+10 e f(x)=

p

x^2 +4 f f(x)=

p

x^2 ¡ 4

g f:x 7! 5 x¡ 3 x^2 h f:x 7 !x+

1

x

i y=

x+4

x¡ 2

j y=x^3 ¡ 3 x^2 ¡ 9 x+10 k f:x 7!

3 x¡ 9

x^2 ¡x¡ 2

l y=x^2 +x¡^2

m y=x^3 +

1

x^3

n f:x 7 !x^4 +4x^3 ¡ 16 x+3

DOMAIN AND

RANGE

p

x¡ 5 is defined when x¡ 5 > 0

) x> 5

) the domain is fx:x> 5 g.

A square root cannot be negative.

) the range is fy:y> 0 g.

1

x¡ 5

is defined when x¡ 56 =0

) x 6 =5

) the domain is fx:x 6 =5g.

No matter how large or smallxis, y=f(x) is

never zero.

) the range is fy:y 6 =0g.

1

p

x¡ 5

is defined when x¡ 5 > 0

) x> 5

) the domain is fx:x> 5 g.

y=f(x) is always positive and never zero.

) the range is fy:y> 0 g.

y

5 x

y = ~`x` #-` `5

O

y

5 x

O

1_____________

y = ^^^^

x - 5__

y

5 x

y=

1

p

x¡ 5

O

4037 Cambridge

cyan magenta yellow black Additional Mathematics

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\CAM4037\CamAdd_02\045CamAdd_02.cdr Thursday, 19 December 2013 2:34:54 PM BRIAN