IGCSE Math RevisionQuestion 1
\(f(x) = 3x - 5\). Find
(a) \(f(4)\)
(b) \(f(-2)\)
Show the worked answer
- (a) \(3 \times 4 - 5 = 7\)
- (b) \(3 \times (-2) - 5 = -11\)
Answer: (a) \(7\) (b) \(-11\)
Cambridge IGCSE Maths (0580) · Topic 2: Algebra and graphs · 2.13
Cambridge IGCSE Maths 0580 Functions Questions
Functions questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.
- 8 questions
- 8 Extended
- 8 non-calculator
- Free, no sign-in
What the syllabus asks
- 2.13 Functions Extended only
Extended: Function notation, domain and range; Inverse functions f⁻¹(x); Composite functions gf(x) = g(f(x)).
Summarised in our own words: check the exact wording in the official 0580 syllabus.
Functions questions: Extended
Extended content, for Papers 2 and 4.
Question 2
\(g(x) = x^2 + 1\). Find \(g(-3)\).
Show the worked answer
- \((-3)^2 + 1 = 9 + 1 = 10\)
Answer: \(10\)
Question 3
\(f(x) = 2x + 3\). Find \(f^{-1}(x)\).
Show the worked answer
- Write \(y = 2x + 3\) and swap: \(x = 2y + 3\).
- \(y = \frac{x - 3}{2}\)
Answer: \(f^{-1}(x) = \frac{x - 3}{2}\)
Question 4
\(f(x) = 2x + 3\) and \(g(x) = x^2\).
(a) Find \(fg(2)\).
(b) Find \(gf(x)\) in its expanded form.
Show the worked answer
- (a) \(g(2) = 4\), then \(f(4) = 11\).
- (b) \(gf(x) = (2x + 3)^2 = 4x^2 + 12x + 9\).
Answer: (a) \(11\) (b) \(4x^2 + 12x + 9\)
Question 5
\(h(x) = \frac{x + 4}{3}\). Solve \(h(x) = 5\).
Show the worked answer
- \(\frac{x + 4}{3} = 5\), so \(x + 4 = 15\).
Answer: \(x = 11\)
Question 6
\(f(x) = \frac{1}{x - 2}\).
(a) Which value of \(x\) must be excluded from the domain of \(f\)?
(b) Find \(f^{-1}(x)\).
Show the worked answer
- (a) The denominator is \(0\) when \(x = 2\).
- (b) \(x = \frac{1}{y - 2}\), so \(y - 2 = \frac{1}{x}\) and \(y = \frac{1}{x} + 2\).
Answer: (a) \(x = 2\) (b) \(f^{-1}(x) = \frac{1}{x} + 2\)
Question 7
\(f(x) = x^2 - 1\) for \(x \ge 0\). Write down the range of \(f\).
Show the worked answer
- For \(x \ge 0\), \(x^2\) takes every value from \(0\) upwards, so \(x^2 - 1\) takes every value from \(-1\) upwards.
Answer: \(f(x) \ge -1\)
Question 8
\(f(x) = 3x + 1\). Solve \(ff(x) = 22\).
Show the worked answer
- \(ff(x) = 3(3x + 1) + 1 = 9x + 4\)
- \(9x + 4 = 22\), so \(x = 2\).
Answer: \(x = 2\)
Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).
Keep going
- Algebra and graphs practice for 0580: more questions, each one marked, tagged Core or Extended
- My mistakes, then a Skill Builder on the skills you missed
- Common mistakes in 0580: what the Cambridge examiner reports say
- Algebra and graphs revision notes and the 0580 formula sheet
- Cambridge IGCSE Maths 0580 past papers, when you are ready for a full paper
Questions students ask
Which Cambridge 0580 papers can test functions?
Functions is Extended content (syllabus 2.13), so it is tested only on the Extended papers, Paper 2 (non-calculator) and Paper 4 (calculator). Core candidates do not need it.
Are these Cambridge past-paper questions?
No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.
Where can I practise more functions questions?
In the 0580 practice for topic 2 (Algebra and graphs), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.