1 Numbers and the number system

1.1 Integers

1.2 Fractions

1.3 Decimals

1.4 Powers and roots

1.5 Set language and notation

1.6 Percentages

1.7 Ratio and proportion

1.8 Degree of accuracy

1.9 Standard form

1.10 Applying number

1.11 Electronic calculators

2 Equations, formulae and identities

2.1 Use of symbols

2.2 Algebraic manipulation

2.3 Expressions and formulae

2.4 Linear equations

2.5 Proportion

2.6 Simultaneous linear equations

2.7 Quadratic equations

2.8 Inequalities

3 Sequences, functions and graphs

3.1 Sequences

3.2 Function notation

3.3 Graphs

3.4 Calculus

4 Geometry and trigonometry

4.1 Angles, lines and triangles

4.2 Polygons

4.3 Symmetry

4.4 Measures

4.5 Construction

4.6 Circle properties

4.7 Geometrical reasoning

4.8 Trigonometry and Pythagoras’ theorem

4.9 Mensuration of 2D shapes

4.10 3D shapes and volume

4.11 Similarity

5 Vectors and transformation geometry

5.1 Vectors

5.2 Transformation geometry

6 Statistics and probability

6.1 Graphical representation of data

6.2 Statistical measures

6.3 Probability

IGCSE Math a 3.2 Function notation Topic Practice

Edexcel IGCSE Math a 3.2 Function notation question practice helps you revise this syllabus point with the course map in view. Use this page to focus on one topic, check the style of questions available, and connect each attempt back to the knowledge area it is testing.

EduNinja keeps Math a practice aligned to Edexcel, so you can move from topic review into exam-style question bank work without losing the syllabus structure. Start with a small set, mark the weak steps, then return to nearby topic links when a definition, graph, calculation, or explanation needs repair.

[Maximum number: 9]

The functions f and g are defined as

\begin{aligned} & \mathrm{f}: x \mapsto 5 x-7 \\ & \mathrm{~g}: x \mapsto \frac{5 x}{x+4} \end{aligned}

(a)

Write down the value of x that must be excluded from any domain of g

[ 1 ]

(b)

Find $\operatorname{gf(2.6)}$

[ 2 ]

(c)

Solve fg(x)=2

[ 3 ]

(d)

Express the inverse function $\mathrm{g}^{-1}$ in the form $\mathrm{g}^{-1}: x \mapsto \ldots$

\mathrm{g}^{-1}: x \mapsto

[ 3 ]

[Maximum number: 7]

The functions f and g are such that

\begin{aligned} & \mathrm{f}: x \mapsto 5 x+7 \\ & \mathrm{~g}: x \mapsto \frac{5}{2 x-9} \end{aligned}

(a)

State which value of x cannot be included in any domain of g

[ 1 ]

(b)

Find fg(4)

The function h is such that

\mathrm{h}: x \mapsto 3 x^{2}-12 x+8 \quad \text { where } x>2

[ 2 ]

(c)

Express the inverse function $\mathrm{h}^{-1}$ in the form $\mathrm{h}^{-1}: x \mapsto \ldots$

\mathrm{h}^{-1}: x \mapsto

[ 4 ]

[Maximum number: 4]

The function f is such that $\mathrm{f}(x)=\frac{k}{x}$ where $x \neq 0$ and k is an integer.

(a)

Express the inverse function $\mathrm{f}^{-1}$ in the form $\mathrm{f}^{-1}(x)=\ldots$

\mathrm{f}^{-1}(x)=

The function g is such that $\mathrm{g}(x)=2-3 x^{4}$ where $x \neq 0$
The function h is such that $\mathrm{h}(x)=\frac{3 x}{2-x}$ where $x \neq 2$

[ 1 ]

(b)

Find g(-2)

[ 1 ]

(c)

Express the composite function hg in the form $\mathrm{hg}(x)=\ldots$

Give your answer in its simplest form.

\operatorname{hg}(x)=

[ 2 ]

[Maximum number: 3]

The function f is such that

f(x)=\frac{2}{3 x-5} \quad \text { where } x \neq \frac{5}{3}

(a)

Find $\mathrm{f}\left(\frac{1}{3}\right)$

[ 1 ]

(b)

Find $f^{-1}(x)$

\mathrm{f}^{-1}(x)=

The function g is such that

g(x)=5 x^{2}-20 x+23

[ 2 ]

[Maximum number: 4]

f is the function such that f(x)=4-3 x

(a)

Work out f(5)
g is the function such that $\mathrm{g}(x)=\frac{1}{1-2 x}$

[ 1 ]

(b)

Find the value of x that cannot be included in any domain of g

[ 1 ]

(c)

Work out fg(-1.5)

[ 2 ]

[Maximum number: 4]

The function f is defined as

\mathrm{f}: x \mapsto \frac{3 x+1}{x-2}

(a)

State the value of x that cannot be included in any domain of the function f

[ 1 ]

(b)

Express the inverse function $\mathrm{f}^{-1}$ in the form $\mathrm{f}^{-1}(x)=\ldots$

\mathrm{f}^{-1}(x)=

[ 3 ]

[Maximum number: 4]

The function f is such that $\mathrm{f}(x)=(x-4)^{2}$ for all values of x.

(a)

Find f(1)

[ 1 ]

(b)

State the range of the function f .

The function g is such that $\mathrm{g}(x)=\frac{4}{x+3} \quad x \neq-3$

[ 1 ]

(c)

Work out fg(2)

[ 2 ]

[Maximum number: 3]

The functions f and g are such that

\begin{aligned} & f(x)=3 x-4 \text { where } x>2 \\ & g(x)=\frac{x}{2 x+1} \end{aligned}

(a)

State the value of x that cannot be included in any domain of g

[ 1 ]

(b)

Find $\operatorname{gf}(x)$

Give your answer in its simplest form.

\operatorname{gf}(x)=

[ 2 ]

[Maximum number: 6]

The functions f and g are defined as

\mathrm{f}(x)=\frac{x}{4 x-3} \text { and } \mathrm{g}(x)=x-5

(a)

State which value of x must be excluded from any domain of the function f.

[ 1 ]

(b)

Find fg(x).

Simplify your answer.

\operatorname{fg}(x)=

[ 2 ]

(c)

Express the inverse function $\mathrm{f}^{-1}$ in the form $\mathrm{f}^{-1}(x)=\ldots$

\mathrm{f}^{-1}(x)=

Part of the curve with equation y=h(x) is shown on the grid.

[ 3 ]

[Maximum number: 9]

The functions f and g are defined as

\begin{aligned} & f(x)=x^{2}+6 \\ & g(x)=x-10 \end{aligned}

(a)

Find fg(3)

[ 2 ]

(b)

Solve the equation fg(x)=f(x)

Show clear algebraic working.

The function h is defined as

\mathrm{h}(x)=\frac{2 x-4}{x}

[ 3 ]

(c)

State the value of x that cannot be included in the domain of h

[ 1 ]

(d)

Express the inverse function $\mathrm{h}^{-1}$ in the form $\mathrm{h}^{-1}(x)=\ldots$

\mathrm{h}^{-1}(x)=

[ 3 ]

0 selected

Question 16

Question 16(a)

Question 16(b)

Question 16(c)

Question 16(d)

Question 19

Question 19(a)

Question 19(b)

Question 19(c)

Question 18

Question 18(a)

Question 18(b)(i)

Question 18(b)(ii)

Question 16

Question 16(a)

Question 16(b)

Question 17

Question 17(a)

Question 17(b)

Question 17(c)

Question 15

Question 15(a)

Question 15(b)

Question 17

Question 17(a)

Question 17(b)

Question 17(c)

Question 19

Question 19(a)

Question 19(b)

Question 18

Question 18(a)

Question 18(b)

Question 18(c)

Question 17

Question 17(a)

Question 17(b)

Question 17(c)

Question 17(d)