
Initial Diagnostic Audit  Unit G4: Functions 
Section G4.1  Functions, Mappings and Domains

1. 
The function f is defined by f : x
→ x^{3}  x for all x.
(a) What is f(1)?
(b) What is f(1)?
(c) Is f a 1 : 1 mapping?

2. 
The function f(x) = 
x^{4}  16 

x  2 
(a) What is the value of f(4)?
(b) What is the value of x for which f(x) = 0?

Section G4.2  Composite Functions

3. 
The functions f and g are defined by
f : x → 
x  1  g : x → 
x  (x ≠ 1) 
 
x + 1  2 
(a) f(2) = 


(c) gf(2) = 


(d) fg(2) =

4. 
f : x → x + 2 and
g : x → x  2
Does fg(x) =
gf(x) for all x?

Section G4.3  Inverse Functions 
5. 
The functions f and g are defined by
f : x → 2x + 1 g : x → 
1  (x  1) 

2 
(a) fg(1) =
(b) gf(1) =
(c) Are f and g inverse functions?

6. 
The function f is defined by
f(x) = 
3x + 2  (x ≠ 1) 

x  1 
and its inverse is of the form
f ^{1}(x) = 
ax + 2 

x + b 
when a and b are constants.
(a) a =
(b) b =

Section G4.4  Transformations of Graphs of Functions 
7. 
The graph below illustrates the function y = f(x) by a dashed line.
What are the equations of the other functions?
(a) Function A y = f ()
(b) Function B y = f ()
(c) Function C y = f ()

8. 
The graph of y = cosx for 0° ≤ x ≤ 360° is given below.
Give the equation of each of the transformed graphs. In each case the graph of y = cosx is shown dotted to help you.
