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46 | P a g e

(a) Sketch the graph of f

(b) Hence, find the domain and range of f



27. (a) Given ( )f x  4(3 ln2 )and ( )g x  e 3 bx , where b is a constant
x
2
(i) Write down an expression for ( f g )( )
x
(ii) Find the value of b such that f and g are inverses of each other


2
4
(b) Find the value of (2)h given that (h g )( ) 4x  4x  and ( )g x  2x  1
x

x
x
x
x
28. Given f ( ) 2 2x , find f  1 ( ) . Hence, sketch f ( ) and f  1 ( ) on the same graph.

29. (a) Given ( )f x  6x  p , find the function g for each of the composite function below,
(i)  f g ( ) 8x  x  2 5
2
2
(ii) g f ( )x  36x  12px  p

2
(b) Given ( )f x  x  2x  where x  1, find the value of f  1 (6) .
3

30. Given the functions as follows:

x
g ( ) e x 3

x
1)
f ( )  2 ln(x 
(a) In a separate diagram, sketch the graph ( )g x and ( )f x . Hence, state the domain and
range for each of the function f and g .

(b) Find  f g ( )x . Hence, solve for x such that  f g ( )x  .
2


1 2x
2
31. If g f   x  , x   and   3 2f x   x. Find   x
g

2 x


2
f
13  and   3f
32. Given that function   x  p qx such that f   5  17 . Find the
exact values of p and q.


33. Given two functions   lnf x  x m and ( )g x  e x 2 .
(a) If f  1   x  g ( ) , show that the value of m is 2. Hence, find the domain and
x
range for functions ( )g x and g  1 ( ).
x