Cambridge Additional Mathematics

58 Functions (Chapter 2)

EXERCISE 2G

1 If y=f(x) has an inverse function, sketch y=f¡^1 (x), and state the domain and

range of f(x) and f¡^1 (x).

abc

de f

gh i

2 Which of the functions in 1 is a self-inverse function?

3

4 For each of the following functionsf:

i On the same set of axes, sketch y=x, y=f(x), and y=f¡^1 (x).

ii Find f¡^1 (x) using variable interchange.

a f:x 7! 3 x+1 b f:x 7 !x+2

4

5 For each of the following functionsf:

i Find f¡^1 (x).

ii Sketch y=f(x), y=f¡^1 (x), and y=x on the same set of axes.

iii Show that (f¡^1 ±f)(x)=(f±f¡^1 )(x)=x, the identity function.

a f:x 7! 2 x+5 b f:x 7 !x+3 c f:x 7!

x+6

2

6 Given f(x)=2x¡ 5 , find (f¡^1 )¡^1 (x). What do you notice?

7 Sketch the graph of f:x 7 !x^3 and its inverse function f¡^1 (x).

8 Given f:x 7!

1

x

, x 6 =0, find f¡^1 algebraically and show thatfis a self-inverse function.

PRINTABLE

GRAPHS

y

-2 x

5

y = f(x)

O

y

x

(^2) y = (x)¡¦
O
y
x
-3
1
y = (x)¡¦
O
y
x
y = (x)¡¦
4
-2
O
y
x
1
y = (x)¡¦
O
y
x
2
2
y = (x)¡¦
O
y
x
y = (x)¡¦
1
O
y
x
4
y = (x)¡¦
O
y
x
y = (x)¡¦
O
3
If the domain of H(x) is fx:¡ 26 x< 3 g, state the range of H¡^1 (x).
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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_02\058CamAdd_02.cdr Thursday, 30 January 2014 2:29:32 PM BRIAN