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44 | P a g e

(b) Solve the equation ( f g )( )  2.
x

(c) Sketch the graph of   x and determine whether the function is one-to-one. Hence,
f
f
state the domain and range of   x .

16. Given the function   3f x   x  1.Sketch  ,f x hence, determine the domain and range

of the function.

17. Given   log and f x  3 x g   3 .x  x

(a) Show that f and g are one-to-one functions. Without finding the inverse function,
show that the functions f and g are inverses of each other.

(b) On the same axes, sketch the graphs of f and g. Clearly label all intercepts and

lines of symmetry. Hence, state the domain and range of each function.

f
x
18. Given   x  2x 1 and g   x   4.
f
(a) Write   x as a piecewise function.
Hence, find the function   2h x  f   3x  g  .x

(b) Sketch the graph of h.

k
(c) Find the function   x if g k x    x  2 where x  2.Hence, determine the

value of x such that k 1    11.x 


e 2 px
19. A function f and g are defined as f ( )  x  5 2 ln3x  and ( )g x  respectively,
3
(a) write down an expression for f g ( )
x
(b) Find the value of p such that f and g are inverse functions.

 4 , x   1

2

20. Given ( )f x   x  3 , x  1
  x 
 2 x , 1

(a) Sketch the graph of ( )f x and hence, find the range of ( )f x