Cambridge Additional Mathematics

Functions (Chapter 2) 49

4 Determine whether the following statements are true or false:

a If y=f(x) is one-one, then y=jf(x)j is one-one.

b If y=f(x) is not one-one, then y=jf(x)j is not one-one.

c The graphs of y=f(x) and y=jf(x)j always meet thex-axis at the same point(s).

d The graphs of y=f(x) and y=jf(x)j always meet they-axis at the same point.

Example 11 Self Tutor

Draw the graph of y=j 3 x+3j.

We first draw the graph of y=3x+3.

The part of the graph that is below thex-axis is then

reflected in thex-axis to produce y=j 3 x+3j.

5 Draw the graph of:

a y=jxj b y=jx+3j c y=j 6 ¡ 2 xj

d y=j 3 x+1j e y=j 10 ¡ 4 xj f y=

̄

̄^1

2 x+2

̄

̄

Given f:x 7 !f(x) and g:x 7 !g(x), thecomposite functionoffandgwill convert

xintof(g(x)).

f±g or fgis used to represent the composite function offandg. It means “ffollowingg”.

(f±g)(x) or fg(x)=f(g(x))

Consider f:x 7 !x^4 and g:x 7! 2 x+3.

f±g means thatgconvertsxto 2 x+3and then fconverts (2x+3)to (2x+3)^4.

So, (f±g)(x)=(2x+3)^4.

E Composite functions

Notice how

is following.

f

g

y

x

y=3x+3

y = |3x + 3|

-3

-3

3

O

I double

and then

add 3

I raise a

number to

the power 4

x

2x + 3

2x + 3

(2x + 3)\\ 4

g-function machine

f-function machine

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_02\049CamAdd_02.cdr Thursday, 5 December 2013 9:26:16 AM GR8GREG