Cambridge International Mathematics

Introduction to functions (Chapter 19) 389

So, fwould convert 2 into 2(2)¡1=3 and

¡ 4 into 2(¡4)¡1=¡ 9 :

f(x) is read as

‘fofx’. It is

sometimes called

theimageofx.

This function can be written as: f: x 7! 2 x¡ 1 or as f(x)=2x¡ 1.

functionf such that x maps onto 2 x¡ 1

If f(x) is the value ofyfor a given value ofx, then y=f(x).

Notice that for f(x)=2x¡ 1 ;f(2) = 2(2)¡1=3 and

f(¡4) = 2(¡4)¡1=¡ 9 :

Consequently, f(2) = 3 indicates that the point(2,3)

lies on the graph of the function.

Likewise, f(¡4) =¡ 9 indicates that the

point(¡ 4 ,¡9)also lies on the graph.

Example 4 Self Tutor

If f:x 7! 3 x^2 ¡ 4 x, find the value of: a f(2) b f(¡5)

a f(2)

= 3(2)^2 ¡4(2) freplacingxby(2)g

=3£ 4 ¡ 8

=4

b f(¡5)

=3(¡5)^2 ¡4(¡5) freplacingxby(¡5)g

= 3(25) + 20

=95

Example 5 Self Tutor

If f(x)=4¡ 3 x¡x^2 , find in simplest form: a f(¡x) b f(x+2)

a f(¡x)

=4¡3(¡x)¡(¡x)^2

freplacingxby(¡x)g

=4+3x¡x^2

b f(x+2)

=4¡3(x+2)¡(x+2)^2

freplacingxby(x+2)g

=4¡ 3 x¡ 6 ¡

¡

x^2 +4x+4

¢

=¡ 2 ¡ 3 x¡x^2 ¡ 4 x¡ 4

=¡x^2 ¡ 7 x¡ 6

C FUNCTION NOTATION [3.1, 3.6]

x

2 ¡-1x

I double

the input

and then

subtract 1

The machine alongside has been

programmed to perform a particular

function.

If is used to represent this function,

we say that ‘ is the function that

will convert into ’.

f

f

xx 21 ¡

If is fed into

the machine,

comes out.

3

2(3) 1 = 5¡

y

x

()2 ¡3,

()-4 -9,

ƒ()xx¡=¡2 -1

O

36

3

-3

-6

-9

-6 -3

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y:\HAESE\IGCSE01\IG01_19\389IGCSE01_19.CDR Wednesday, 8 October 2008 10:21:40 AM PETER