igureMaths
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Browse Functions
37 questions at your level
Difficulty
All
Level 2
Level 3
Level 4
Level 5
Function notation
14 questions
Lesson
Not started
Mark as done
g
(
x
)
=
x
2
+
1
g(x) = x^2 + 1
g
(
x
)
=
x
2
+
1
(a)
Work out
g
(
−
3
)
g(-3)
g
(
−
3
)
(b)
Solve
g
(
x
)
=
50
g(x) = 50
g
(
x
)
=
50
●●●●
●
Level 4
3 marks
Start
→
Mark as done
f
(
x
)
=
5
−
2
x
f(x) = 5 - 2x
f
(
x
)
=
5
−
2
x
(a)
Work out
f
(
0.5
)
f(0.5)
f
(
0.5
)
(b)
Solve
f
(
x
)
=
x
f(x) = x
f
(
x
)
=
x
●●●●
●
Level 4
3 marks
Start
→
Mark as done
f
(
x
)
=
x
2
−
3
x
f(x) = x^2 - 3x
f
(
x
)
=
x
2
−
3
x
(a)
Work out
f
(
5
)
f(5)
f
(
5
)
(b)
Solve
f
(
x
)
=
0
f(x) = 0
f
(
x
)
=
0
●●●●
●
Level 4
3 marks
Start
→
Mark as done
h
(
x
)
=
12
x
h(x) = \dfrac{12}{x}
h
(
x
)
=
x
12
for
x
≠
0
x \neq 0
x
=
0
(a)
Work out
h
(
8
)
h(8)
h
(
8
)
(b)
Work out
h
(
−
4
)
h(-4)
h
(
−
4
)
(c)
Solve
h
(
x
)
=
5
h(x) = 5
h
(
x
)
=
5
●●●●
●
Level 4
4 marks
Start
→
Mark as done
f
(
x
)
=
x
2
+
2
x
f(x) = x^2 + 2x
f
(
x
)
=
x
2
+
2
x
(a)
Work out
f
(
−
3
)
f(-3)
f
(
−
3
)
(b)
Solve
f
(
x
)
=
15
f(x) = 15
f
(
x
)
=
15
●●●●
●
Level 4
5 marks
Start
→
Mark as done
The functions f and g are given by
f
(
x
)
=
18
x
−
2
and
g
(
x
)
=
7
−
4
x
\mathrm{f}(x) = \frac{18}{x - 2} \qquad \text{and} \qquad \mathrm{g}(x) = 7 - 4x
f
(
x
)
=
x
−
2
18
and
g
(
x
)
=
7
−
4
x
(a)
Find
f
(
−
4
)
\mathrm{f}(-4)
f
(
−
4
)
(1 mark)
(b)
Find
f
g
(
−
1
)
\mathrm{fg}(-1)
fg
(
−
1
)
(2 marks)
(c)
Find
g
−
1
(
15
)
\mathrm{g}^{-1}(15)
g
−
1
(
15
)
(2 marks)
●●●●
●
Level 4
5 marks
Start
→
Composite functions
16 questions
Lesson
Not started
Mark as done
f
(
x
)
=
2
x
+
1
f(x) = 2x + 1
f
(
x
)
=
2
x
+
1
and
g
(
x
)
=
x
2
−
3
g(x) = x^2 - 3
g
(
x
)
=
x
2
−
3
(a)
Work out
f
g
(
3
)
fg(3)
f
g
(
3
)
(b)
Work out
g
f
(
3
)
gf(3)
g
f
(
3
)
●●●●
●
Level 4
4 marks
Start
→
Mark as done
f
(
x
)
=
x
2
f(x) = x^2
f
(
x
)
=
x
2
and
g
(
x
)
=
2
x
−
1
g(x) = 2x - 1
g
(
x
)
=
2
x
−
1
(a)
Find
f
g
(
x
)
fg(x)
f
g
(
x
)
(b)
Show that
f
g
(
2
)
≠
g
f
(
2
)
fg(2) \neq gf(2)
f
g
(
2
)
=
g
f
(
2
)
●●●●
●
Level 4
4 marks
Start
→
Mark as done
f
(
x
)
=
12
x
f(x) = \dfrac{12}{x}
f
(
x
)
=
x
12
for
x
≠
0
x \neq 0
x
=
0
, and
g
(
x
)
=
x
+
2
g(x) = x + 2
g
(
x
)
=
x
+
2
(a)
Work out
f
g
(
4
)
fg(4)
f
g
(
4
)
(b)
Work out
g
f
(
4
)
gf(4)
g
f
(
4
)
(c)
Solve
f
g
(
x
)
=
3
fg(x) = 3
f
g
(
x
)
=
3
●●●●
●
Level 4
6 marks
Start
→
Mark as done
f
(
x
)
=
2
x
+
3
g
(
x
)
=
x
2
−
1
\mathrm{f}(x) = 2x + 3 \qquad \mathrm{g}(x) = x^2 - 1
f
(
x
)
=
2
x
+
3
g
(
x
)
=
x
2
−
1
(a)
Show that
g
f
(
x
)
=
4
x
2
+
12
x
+
8
\mathrm{gf}(x) = 4x^2 + 12x + 8
gf
(
x
)
=
4
x
2
+
12
x
+
8
(2 marks)
(b)
Solve
g
f
(
x
)
=
8
\mathrm{gf}(x) = 8
gf
(
x
)
=
8
(2 marks)
●●●●
●
Level 4
4 marks
Start
→
Mark as done
f
(
x
)
=
3
x
−
1
g
(
x
)
=
x
2
+
1
\mathrm{f}(x) = 3x - 1 \qquad \mathrm{g}(x) = x^2 + 1
f
(
x
)
=
3
x
−
1
g
(
x
)
=
x
2
+
1
(a)
Work out
f
g
(
2
)
\mathrm{fg}(2)
fg
(
2
)
. [2]
(b)
Solve
f
g
(
x
)
=
g
f
(
x
)
\mathrm{fg}(x) = \mathrm{gf}(x)
fg
(
x
)
=
gf
(
x
)
. [3]
●●●●
●
Level 4
5 marks
Start
→
Mark as done
The functions f and g are given by
f
(
x
)
=
18
x
−
2
and
g
(
x
)
=
7
−
4
x
\mathrm{f}(x) = \frac{18}{x - 2} \qquad \text{and} \qquad \mathrm{g}(x) = 7 - 4x
f
(
x
)
=
x
−
2
18
and
g
(
x
)
=
7
−
4
x
(a)
Find
f
(
−
4
)
\mathrm{f}(-4)
f
(
−
4
)
(1 mark)
(b)
Find
f
g
(
−
1
)
\mathrm{fg}(-1)
fg
(
−
1
)
(2 marks)
(c)
Find
g
−
1
(
15
)
\mathrm{g}^{-1}(15)
g
−
1
(
15
)
(2 marks)
●●●●
●
Level 4
5 marks
Start
→
Inverse functions
13 questions
Lesson
Not started
Mark as done
f
(
x
)
=
2
x
+
5
f(x) = 2x + 5
f
(
x
)
=
2
x
+
5
Find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
●●●●
●
Level 4
2 marks
Start
→
Mark as done
g
(
x
)
=
x
−
4
3
g(x) = \dfrac{x - 4}{3}
g
(
x
)
=
3
x
−
4
(a)
Find
g
−
1
(
x
)
g^{-1}(x)
g
−
1
(
x
)
(b)
Work out
g
−
1
(
2
)
g^{-1}(2)
g
−
1
(
2
)
●●●●
●
Level 4
3 marks
Start
→
Mark as done
f
(
x
)
=
x
4
+
3
f(x) = \dfrac{x}{4} + 3
f
(
x
)
=
4
x
+
3
(a)
Find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
(b)
Work out
f
−
1
(
5
)
f^{-1}(5)
f
−
1
(
5
)
●●●●
●
Level 4
3 marks
Start
→
Mark as done
g
(
x
)
=
3
(
x
−
2
)
g(x) = 3(x - 2)
g
(
x
)
=
3
(
x
−
2
)
(a)
Find
g
−
1
(
x
)
g^{-1}(x)
g
−
1
(
x
)
(b)
Solve
g
−
1
(
x
)
=
10
g^{-1}(x) = 10
g
−
1
(
x
)
=
10
●●●●
●
Level 4
4 marks
Start
→
Mark as done
f
(
x
)
=
6
x
−
1
f(x) = 6x - 1
f
(
x
)
=
6
x
−
1
(a)
Find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
(b)
Show that
f
(
f
−
1
(
x
)
)
=
x
f\!\left(f^{-1}(x)\right) = x
f
(
f
−
1
(
x
)
)
=
x
●●●●
●
Level 4
4 marks
Start
→
Mark as done
The functions f and g are given by
f
(
x
)
=
18
x
−
2
and
g
(
x
)
=
7
−
4
x
\mathrm{f}(x) = \frac{18}{x - 2} \qquad \text{and} \qquad \mathrm{g}(x) = 7 - 4x
f
(
x
)
=
x
−
2
18
and
g
(
x
)
=
7
−
4
x
(a)
Find
f
(
−
4
)
\mathrm{f}(-4)
f
(
−
4
)
(1 mark)
(b)
Find
f
g
(
−
1
)
\mathrm{fg}(-1)
fg
(
−
1
)
(2 marks)
(c)
Find
g
−
1
(
15
)
\mathrm{g}^{-1}(15)
g
−
1
(
15
)
(2 marks)
●●●●
●
Level 4
5 marks
Start
→