Cambridge International Mathematics

Example 3 Self Tutor

Find the inverse function f¡^1 (x) for: a f(x)=5x b f(x) = 2 log 3 x

a y=5x has inverse function x=5y

) y= log 5 x

So, f¡^1 (x) = log 5 x

b y= 2 log 3 x has inverse function

x= 2 log 3 y

)

x

2

= log 3 y

) y=3

x

2

So, f¡^1 (x)=3

x

2

EXERCISE 31B

1 Find the inverse function f¡^1 (x) for:

a f(x)=4x b f(x)=10x c f(x)=3¡x d f(x)=2£ 3 x

e f(x) = log 7 x f f(x)=^12 (5x) g f(x) = 3 log 2 x h f(x) = 5 log 3 x

i f(x) = logp 2 x

2aOn the same set of axes graph y=3x and y= log 3 x.

b State the domain and range of y=3x.

c State the domain and range of y= log 3 x.

3 Prove using algebra that if f(x)=ax then f¡^1 (x) = logax.

-5 5 x

5

-5

y

OO

y¡=¡2x

yx¡=¡logx

yx¡=¡

If f(x)=g(x),

graph y=f(x)

and y=g(x)

on the same set

of axes.

4 Use the logarithmic function log on your graphics calculator

to solve the following equations correct to 3 significant

figures. You may need to use the instructions on page 15.

628 Logarithms (Chapter 31)

For example, if f(x) = log 2 x then f¡^1 (x)=2x.

The inverse function y= log 2 x is the reflection of y=2x

in the line y=x.

a log 10 x=3¡x b log 10 (x¡2) = 2¡x

c log 10

¡x

4

¢

=x^2 ¡ 2 d log 10 x=x¡ 1

e log 10 x=5¡x f log 10 x=3x¡ 3

IGCSE01

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Y:\HAESE\IGCSE01\IG01_31\628IGCSE01_31.CDR Tuesday, 18 November 2008 11:12:59 AM PETER