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CHAPTER 5 : FUNCTIONS AND GRAPHS


1. Given ( ) 4f x   x 2 , x R .
(a) Sketch the graph of ( )f x .
(b) Hence, state the domain and range of ( )f x .

2. A function f is defined by ( )f x  x  2 1. Sketch the graph of ( )f x and state the domain and

range of ( )f x .


x
2
h
3. Given that f   2x  x  1 and   2x  4x  1 , find the function g such that
 f g   x  h   x . Write g in the form of (a x b )  2 c where a, b and c are constants.

2x
4. Functions f and g are defined as ( )f x  e , ( ) 1g x   x , x  R .
x
Find f  1 ( ) and hence obtain (g f  1 )( )
x

2
3
5. A function f is defined by ( )f x  x  2x  for 0 x  5 . State the range of f and
determine whether f is one to one.

3x

6. Given ( )h x  . Defining h 2 ( ) (h h )( ) , determine the function h 2 ( ) and hence
x
x
x
x  3
deduce the inverse of ( )h x . Evaluate h 13 (9) .

2
0
7. Given ( ) 2f x  x  1 , x  . Defining ( )g x  x  3, find


1
1
(a) the inverse f and g and verify that (g f )  f  1 g
(b) the values of x for which graph of f g  g f


10 2x  x 
2
2
8. Given that ( )f x  and ( ) 5 2g x   x . Fınd the value k so that f  1 ( )  g   .
x
k  2 
Hence, find  f  1 g  (0) .

9. Let ( )f x  4x  1 and ( )g x  x  2 . If ( )  h x f ( ) 2 ( ) , express ( )h x as a piecewise

x
g
x
function.