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10. Let ( )f ax  a x  a x  3a where a is non-zero.
(a) Find a if (0)f  6.

(b) Determine ( )f x .

(c) Determine the domain and range of ( )f x . Hence, state the interval in which f is

one to one

1
x
11. A function g is defined by ( )g x  , x  1.Find g  1 ( ) .
x  1
 x 
12. Given that ( ) lnf x    1 .

 3 
(a) Show that f is one to one function.


x
(b) Find f  1 ( ) and hence, find the value of x when f  1 ( ) 6.
x

13. The functions f and g are defined by

f   x  x  2 1 , x R

g   x  x  1 , x R

(a) Find all the roots of  2 g f    f g x   7x  .

x
(b) Given ( )h x  .
g   x

 
(i) find h h x .

x
(ii) Hence, determine h  1 ( ) .

14. A function f is defined as ( ) 3f x   x  2

x
x
(a) Show that the function f  1 ( ) exists and hence, find f  1 ( ).
(b) State the domain and range of f  1 ( ).
x
(c) On the same axes, sketch the graphs of ( )f x and f  1 ( ).
x
State the relationship between the two graphs.


x
15. Given that f ( ) e  2x 1 and g ( )  x 2x  1.
x
x
(a) Given ( )p x  4x  7.Find the function q such that (g q  1 )( )  p ( ).