GCSE
FUNCTIONS
[ESTIMATED TIME: 75 minutes]
(+ IGCSE) EXAM QUESTION PRACTICE
1.
[8 marks]
11 The functions f and g are defined as
f(x) =
1
x+4
2
g( x) =
2x
x +1
(a) Work out f(6)
.........................................
(1)
(b) Work out fg(–3)
.........................................
(2)
(c) g(a) = –2
Work out the value of a.
a = .........................................
(2)
(d) Express the inverse function f –1 in the form f –1(x) = …
Contains questions which have been reproduced with the kind
permission of Pearson Education Limited UK
f –1( x ) = .........................................
(3)
Questions compiled by:
@Maths4Everyone
(Total for Question 11 is 8 marks)
f –1( x ) = .........................................
(3)
(Total for Question 11 is 8 marks)
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[8 marks]
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3.
[6 marks]
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f : x ! 2x – 1
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(a) Find the value of
(i) f(3),
...............................
(ii) fg(6).
...............................
(2)
(b) Express the inverse function f –1 in the form f –1: x ! ...
...............................
(2)
(c) (i) Express the composite function gf in the form gf : x ! ...
...............................
(ii) Which value of x must be excluded from the domain of gf ?
x = ........................
(2)
(Total 6 marks)
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[7 marks]
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[7 marks]
6.
[6 marks]
16
f(x) =
(a) Find the value of f(11)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .
(1)
(b) State which value of x must be excluded from any domain of f
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x −1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .
(1)
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(c) Find f ––1(x)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .
(d) State the value which cannot be in any range of f
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .
(1)
(Total for Question 16 is 6 marks)
18
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(3)
7.
[7 marks]
18 f is the function such that
(a) Find
x
3x + 1
f (0.5)
.......................................................
(1)
(b) Find
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f(x) =
ff(–1)
(2)
(c) Find the value of x that cannot be included in any domain of f
.......................................................
(1)
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.......................................................
(d) Express the inverse function f –1 in the form f –1(x) = ...
Show clear algebraic working.
(Total for Question 18 is 7 marks)
16
*P45864A01620*
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(3)
8.
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[5 marks]
10.
[7 marks]
21 The function f is defined as f ( x) =
3
4+ x
(a) Find the value of f(1)
...............................
(1)
(b) State which value of x must be excluded from any domain of f.
...............................
(1)
The function g is defined as g(x) = 5 + x
(c) Given that g(a) = 7, find the value of a.
a = ...............................
(1)
(d) Calculate fg(1)
...............................
(2)
(e) Find fg(x)
Simplify your answer.
fg(x) = ...............................
(2)
(Total for Question 21 is 7 marks)
20
*P43028A02024*
11.
[3 marks]
.......................................................
(2)
. .. .. .. .. .. .. .. .. .. .. .. . .. .. .. .. .. .. .. .. .. .. ... .... .... ... ....
(b) Solve 6x + 4 > x + 17
(1)
g is a function such that
g(x) =
x!1
(b) Find fg(x)
Give your answer as simply as possible.
.......................................................
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1
(a) Find f( 2 )
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23 f is a function such that
1
9 (a) Factorise
y2 + 7y + 6
f(x) = 2
x +1
(2)
(c) n is an integer with –5 < 2n - 6
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(Total
Question
marks)
(Total
forfor
Question
239isis36marks)
12.
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................
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.... ... ....
(2)
(2)
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Write down all the values of n
[4 marks]
24
made
10 On
TheMonday,
functionNalim
f is such
thata journey.
On Tuesday, she made the same journey.
Her average speed on Tuesday
f(x) was
= 4x25%
– 1 greater than her average speed on Monday.
Calculate
–1 percentage reduction in the time her journey took on Tuesday compared
(x)
(a) Find fthe
with Monday.
f–1(x) = . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
The function g is such that
g(x) = kx2 where k is a constant.
Given that fg(2) = 12
(b) work out the value of k
.. .. .. ... .... .... .... ... .... .... .... ... .... .... .. ....... .... .... ....... .... .... .......
k.. ..=
. . .....
. . . ....
. . . . . .%
.......
(2)
(Total for Question 24 is 3 marks)
(Total for Question 10 is 4 marks)
10
154
*P41036A01720*
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17
over
Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics - Sample Assessment Materials (SAMs) - Issue 2 -Turn
June 2015
© Pearson Education Limited 2015
13.
24.
Leave
blank
f(x) = x2
g(x) = x – 3
(a) (i) Find gf(x)
.....................................
(ii) Find g –1(x)
.....................................
(2)
(b) Solve the equation gf(x) = g –1(x)
.....................................
(3)
Q24
(Total 5 marks)
*H34884A02324*
23
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[5 marks]