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Edexcel IGCSE Maths (4MA1) · Unit 4: Graphs & Functions

IGCSE Maths Functions Questions and Answers

Functions questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 4 worked examples first, then try the 3 exam-style questions yourself and check your working against the mark scheme.

Practise functions in Unit 4 →Graphs, Sequences and Calculus revision notes

What this topic covers

Functions worked examples

Worked example 1: Function notation

\(\mathrm{f}(x)=2x^2-3\). Find \(\mathrm{f}(-2)\) and solve \(\mathrm{f}(x)=15\).

Solution

  1. \(\mathrm{f}(-2)=2\times4-3=5\).
  2. \(2x^2-3=15\): \(x^2=9\), \(x=\pm3\).

Answer: \(\mathrm{f}(-2)=5\); \(x=\pm3\)

Tip: f(−2) means replace every x with −2.

Worked example 2: Domain and range

(a) Which value is excluded from the domain of \(\mathrm{f}(x)=\dfrac{1}{x-2}\)? (b) State the range of \(\mathrm{g}(x)=x^2+3\).

Solution

  1. (a) The denominator cannot be 0: exclude \(x=2\).
  2. (b) \(x^2\ge0\), so \(\mathrm{g}(x)\ge3\).

Answer: (a) \(x=2\) (b) \(\mathrm{g}(x)\ge3\)

Tip: Domain is the inputs; range is the outputs.

Worked example 3: Composite functions

\(\mathrm{f}(x)=x+4\) and \(\mathrm{g}(x)=3x^2\). Find \(\mathrm{fg}(x)\) and \(\mathrm{fg}(2)\).

Solution

  1. \(\mathrm{fg}(x)\) means apply g first: \(\mathrm{f}(3x^2)=3x^2+4\).
  2. \(\mathrm{fg}(2)=3\times4+4=16\).

Answer: \(3x^2+4\); 16

Tip: fg(x) ≠ gf(x) in general: gf(x) = 3(x + 4)².

Worked example 4: Inverse function

\(\mathrm{f}(x)=\dfrac{2x+1}{5}\). Find \(\mathrm{f}^{-1}(x)\).

Solution

  1. Write \(y=\dfrac{2x+1}{5}\) and swap: \(x=\dfrac{2y+1}{5}\).
  2. \(5x=2y+1\), so \(y=\dfrac{5x-1}{2}\).

Answer: \(\mathrm{f}^{-1}(x)=\dfrac{5x-1}{2}\)

Tip: Check: f⁻¹(f(3)) = f⁻¹(7/5) = 3.

Functions exam-style questions

Try each question before you open the answer. The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.

Question 1 · easy · 3 marks

\( \mathrm{f}(x) = 4 - 3x \). (a) Work out \( \mathrm{f}(-2) \). (b) Find the value of \( x \) for which \( \mathrm{f}(x) = 19 \).

Show the answer and mark scheme
  • B1 10
  • M1 4 − 3x = 19
  • A1 −5

Answer: (a) 10 (b) \( x = -5 \)

Question 2 · medium · 3 marks

\( \mathrm{g}(x) = x^2 - 2x \). Solve \( \mathrm{g}(x) = 15 \).

Show the answer and mark scheme
  • M1 x² − 2x − 15 = 0
  • M1 (x − 5)(x + 3) = 0
  • A1 x = 5, x = −3

Answer: \( x = 5 \) or \( x = -3 \)

Question 3 · hard · 4 marks

\( \mathrm{f}(x) = ax + b \), where \( a \) and \( b \) are constants. \( \mathrm{f}(2) = 11 \) and \( \mathrm{f}(-3) = -9 \). (a) Find the values of \( a \) and \( b \). (b) Solve \( \mathrm{f}(2x) = \mathrm{f}(x) + 20 \).

Show the answer and mark scheme
  • M1 2a + b = 11 and −3a + b = −9
  • A1 a = 4, b = 3
  • M1 8x + 3 = 4x + 3 + 20
  • A1 x = 5

Answer: (a) \( a = 4 \), \( b = 3 \) (b) \( x = 5 \)

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

Revise functions for the exam

Questions students ask

Which Edexcel IGCSE Maths papers test functions?

Either Higher tier paper, 1H or 2H, can test functions: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more functions questions?

In the IGCSE student hub: Unit 4 (Graphs & Functions) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

More Unit 4 topics: Graphs & Functions