1
1
for x > 0
for x > 0
Find the exact solution of
[3]
[Total: 3]
2
for x > 0 .
The range of f is f > 9.
(a) Find
[3]
2
(b) State the domain of
[1]
[Total: 4]
3
for x > 0
Find the range of f.
[1]
[Total: 1]
4
The function g is defined by
Find an expression for g(x)-1 and state its domain and range.
[4]
[Total: 4]
3
5
The function f is defined by
The function g is defined by
Find and simplify an expression for fg(x), and explain why the function gf does not exist.
[3]
[Total: 3]
6
The function f is defined by
Sketch the graph of y = f(x) and hence sketch the graph of y = f−1(x) on the axes below.
[3]
[Total: 3]
4
7
Write down the range of g−1.
[1]
[Total: 1]
8
Find an expression for g−1(x).
[2]
[Total: 2]
9
The function h is defined by
for
.
(a) State the geometrical relationship between the graphs of
and
.
[1]
5
(b) Find an expression for
.
[3]
[Total: 4]
10
The functions h and k are defined by
for
,
for
.
(a) Find hk(10).
[2]
(b) Find
, stating its domain and range.
[5]
[Total: 7]
6
11
(a) On the axes below, sketch the graph of
the graph meets the axes.
showing the coordinates of the points where
[3]
11
(b) Find the coordinates of the stationary point on the curve
.
[2]
(c) Find the values of k such that the equation
has only 2 solutions.
[2]
7
[Total: 7]
12
Functions g and h are defined by
for x ∈,
for
(a) Find
.
.
[2]
(b) Solve
.
[3]
[Total: 5]
8
13
(a)
y
y
A
y
B
O
C
O
x
y
y
D
(i)
F
O
x
x
y
E
O
O
x
O
x
x
Write down the letter of each graph which does not represent a function.
[2]
(ii) Write down the letter of each graph which represents a function that does not have an inverse.
[2]
y
5
y = f(x)
x
O
13
(b) The diagram shows the graph of a function
.
5
. On the same axes sketch the graph of
[2]
[Total: 6]