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37 questions at your level
Difficulty
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Level 2
Level 3
Level 4
Level 5
Function notation
14 questions
Lesson
Not started
Mark as done
f
(
x
)
=
2
x
−
3
f(x) = 2x - 3
f
(
x
)
=
2
x
−
3
and
g
(
x
)
=
x
+
4
g(x) = x + 4
g
(
x
)
=
x
+
4
(a)
Solve
f
(
x
)
=
g
(
x
)
f(x) = g(x)
f
(
x
)
=
g
(
x
)
(b)
The graphs of
y
=
f
(
x
)
y = f(x)
y
=
f
(
x
)
and
y
=
g
(
x
)
y = g(x)
y
=
g
(
x
)
are drawn on the same axes. What does your answer to part (a) tell you about the two graphs?
●●●●●
Level 5
3 marks
Start
→
Mark as done
f
(
x
)
=
2
x
+
3
g
(
x
)
=
4
x
2
−
5
\mathrm{f}(x) = 2x + 3 \qquad \mathrm{g}(x) = 4x^2 - 5
f
(
x
)
=
2
x
+
3
g
(
x
)
=
4
x
2
−
5
Show that
g
f
(
x
)
−
2
f
g
(
x
)
=
0
\mathrm{gf}(x) - 2\mathrm{fg}(x) = 0
gf
(
x
)
−
2
fg
(
x
)
=
0
has just one solution for
x
x
x
.
(5 marks)
●●●●●
Level 5
5 marks
Start
→
Mark as done
f
(
x
)
=
5
x
−
4
h
(
x
)
=
2
x
2
+
x
\mathrm{f}(x) = 5x - 4 \qquad \mathrm{h}(x) = 2x^2 + x
f
(
x
)
=
5
x
−
4
h
(
x
)
=
2
x
2
+
x
Show that
5
f
h
(
x
)
−
h
f
(
x
)
=
0
5\mathrm{fh}(x) - \mathrm{hf}(x) = 0
5
fh
(
x
)
−
hf
(
x
)
=
0
has just one solution for
x
x
x
.
(5 marks)
●●●●●
Level 5
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)
Find
f
g
(
x
)
fg(x)
f
g
(
x
)
, giving your answer in its simplest form.
(b)
Find
g
f
(
x
)
gf(x)
g
f
(
x
)
, giving your answer in its simplest form.
●●●●●
Level 5
4 marks
Start
→
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
Solve
f
g
(
x
)
=
45
fg(x) = 45
f
g
(
x
)
=
45
●●●●●
Level 5
3 marks
Start
→
Mark as done
f
(
x
)
=
2
x
+
1
f(x) = 2x + 1
f
(
x
)
=
2
x
+
1
(a)
Find
f
f
(
x
)
ff(x)
f
f
(
x
)
, giving your answer in its simplest form.
(b)
Solve
f
f
(
x
)
=
23
ff(x) = 23
f
f
(
x
)
=
23
●●●●●
Level 5
4 marks
Start
→
Mark as done
f
(
x
)
=
x
+
3
2
f(x) = \dfrac{x + 3}{2}
f
(
x
)
=
2
x
+
3
and
g
(
x
)
=
4
x
−
1
g(x) = 4x - 1
g
(
x
)
=
4
x
−
1
(a)
Find
f
g
(
x
)
fg(x)
f
g
(
x
)
, giving your answer in its simplest form.
(b)
Solve
f
g
(
x
)
=
17
fg(x) = 17
f
g
(
x
)
=
17
●●●●●
Level 5
4 marks
Start
→
Mark as done
f
(
x
)
=
5
−
x
f(x) = 5 - x
f
(
x
)
=
5
−
x
(a)
Find
f
f
(
x
)
ff(x)
f
f
(
x
)
, giving your answer in its simplest form.
(b)
What does your answer to part (a) tell you about the function
f
f
f
?
●●●●●
Level 5
3 marks
Start
→
Mark as done
f
(
x
)
=
2
x
+
3
g
(
x
)
=
4
x
2
−
5
\mathrm{f}(x) = 2x + 3 \qquad \mathrm{g}(x) = 4x^2 - 5
f
(
x
)
=
2
x
+
3
g
(
x
)
=
4
x
2
−
5
Show that
g
f
(
x
)
−
2
f
g
(
x
)
=
0
\mathrm{gf}(x) - 2\mathrm{fg}(x) = 0
gf
(
x
)
−
2
fg
(
x
)
=
0
has just one solution for
x
x
x
.
(5 marks)
●●●●●
Level 5
5 marks
Start
→
Mark as done
f
(
x
)
=
5
x
−
4
h
(
x
)
=
2
x
2
+
x
\mathrm{f}(x) = 5x - 4 \qquad \mathrm{h}(x) = 2x^2 + x
f
(
x
)
=
5
x
−
4
h
(
x
)
=
2
x
2
+
x
Show that
5
f
h
(
x
)
−
h
f
(
x
)
=
0
5\mathrm{fh}(x) - \mathrm{hf}(x) = 0
5
fh
(
x
)
−
hf
(
x
)
=
0
has just one solution for
x
x
x
.
(5 marks)
●●●●●
Level 5
5 marks
Start
→
Inverse functions
13 questions
Lesson
Not started
Mark as done
h
(
x
)
=
5
x
−
2
h(x) = 5x - 2
h
(
x
)
=
5
x
−
2
Solve
h
−
1
(
x
)
=
3
h^{-1}(x) = 3
h
−
1
(
x
)
=
3
●●●●●
Level 5
3 marks
Start
→
Mark as done
f
(
x
)
=
4
−
x
f(x) = 4 - x
f
(
x
)
=
4
−
x
(a)
Find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
(b)
What do you notice about
f
f
f
and
f
−
1
f^{-1}
f
−
1
?
●●●●●
Level 5
3 marks
Start
→
Mark as done
f
(
x
)
=
3
x
−
1
x
+
2
f(x) = \dfrac{3x - 1}{x + 2}
f
(
x
)
=
x
+
2
3
x
−
1
Find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
●●●●●
Level 5
3 marks
Start
→
Mark as done
f
(
x
)
=
10
x
−
3
f(x) = \dfrac{10}{x - 3}
f
(
x
)
=
x
−
3
10
for
x
≠
3
x \neq 3
x
=
3
Find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
●●●●●
Level 5
3 marks
Start
→
Mark as done
f
(
x
)
=
2
x
+
c
f(x) = 2x + c
f
(
x
)
=
2
x
+
c
, where
c
c
c
is a constant.
f
−
1
(
11
)
=
4
f^{-1}(11) = 4
f
−
1
(
11
)
=
4
Work out the value of
c
c
c
.
●●●●●
Level 5
3 marks
Start
→