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47 | P a g e

(b) Given ( )h x  x  3 , x  3, find h  1   1 . Hence, find g h  1 (1) .

34. Given

f   x   1, x  5
x

g   x  , x x  0

(a) Write down an expression for the composite function g f  .x

(b) Find the expression for each of the following inverse functions

(i) f  1   x

1
(ii) g f    x
1

x
(c) Verify that g f     f  1 g  1   x . Hence, find the domain and range for
 1
g f    x .
35. (a) Given that   lnf x  3x   2

(i) Show that   x is one-to-one.
f
(ii) Find the inverse function of   x .
f

(iii) State the domain and range of   x and f  1   x .
f

13 log x

(b) Given two functions   7f x  4x m and   x  7 . If   x and   x are
f
g
g
n
inverse of each other, express in terms of and .