Cambridge Additional Mathematics

Functions (Chapter 2) 43

11 Given f(x)=ax+

b

x

, f(1) = 1, and f(2) = 5, find constantsaandb.

12 Given T(x)=ax^2 +bx+c, T(0) =¡ 4 , T(1) =¡ 2 , and T(2) = 6, finda,b, andc.

Thedomainof a relation is the set of values ofxin the relation.

Therangeof a relation is the set of values ofyin the relation.

The domain and range of a relation are often described usinginterval notation.

For example:

(1) All values of x>¡ 1 are included,

so the domain is fx:x>¡ 1 g.

All values of y>¡ 3 are included,

so the range is fy:y>¡ 3 g.

(2) xcan take any value,

so the domain is fx:x 2 Rg.

ycannot be> 1 ,

so the range is fy:y 61 g.

(3) xcan take all values except 2 ,

so the domain is fx:x 6 =2g.

ycan take all values except 1 ,

so the range is fy:y 6 =1g.

DOMAIN AND RANGE OF FUNCTIONS

To fully describe a function, we need both a ruleanda domain.

For example, we can specify f(x)=x^2 where x> 0.

If a domain is not specified, we use thenatural domain, which is the largest part ofR for whichf(x)is

defined.

C Domain and range

The range is sometimes

called theimage set.

(2 1),¡

y

x

O

(-1 -3),

O

y

x

y

y=1

x=2

O x

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_02\043CamAdd_02.cdr Thursday, 19 December 2013 5:03:14 PM BRIAN