Cambridge Additional Mathematics

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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

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

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