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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100 100 4037 Cambridge
Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_02\058CamAdd_02.cdr Thursday, 30 January 2014 2:29:32 PM BRIAN