plumiFunctions, inverse and composite functions: AQA GCSE Maths questions
Every AQA GCSE Maths exam question on A7 Functions, inverse and composite functions, 2017–2025, with its mark scheme and examiner’s report.
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All 24 questions on Functions, inverse and composite functions, as a list
- June 2025, Paper 2H, Q25 (4 marks): f(x) = ax + b and g(x) = x b a + where a and b are positive integers. Prove that fg(x) – a f –1(x) is always a multiple of 3
- November 2024, Paper 1H, Q2 (3 marks): (a) Complete this number machine so that y = 4x + 5 2 (b) Complete this number machine so that y = 3x – 24 2 (c) Complete this number machine so that y = x
- June 2024, Paper 3H, Q19 (6 marks): f(x) = x – 3 g(x) = 4x – 7 19 (a) Work out the value of fg Answer 19 (b) Solve (f(x))2 = g(x) Answer
- November 2023, Paper 1H, Q21 (5 marks): f(x) = 8 9 − x g(x) = 2x2 + 9 h(x) = 4x Solve f –1(x) = gh(x) Answer
- June 2023, Paper 1H, Q13 (4 marks): (a) Here is a number machine. Show that when the input increases by 2 the output increases by 2a. 13 (b) f(x) = kx2 where k is a constant. Kai says that f f is
- June 2023, Paper 3H, Q18 (6 marks): f(x) = x2 + 6x g(x) = 2x + 4 18 (a) Show that fg(x) = 4x2 + 28x + 40 18 (b) Solve fg(x) = –5 Answer
- November 2022, Paper 2H, Q21 (4 marks): f(x) = 5 9 3 + x and g(x) = 6x – 1 21 (a) Show that gf is an integer. 21 (b) Show that f –1 is not an integer.
- June 2022, Paper 2H, Q25 (4 marks): f(x) = 2x + 5 Show that 3f(x) – 12f –1(x) simplifies to an integer.
- June 2022, Paper 3H, Q22 (1 mark): f(x) = 3x and g(x) = x2 Circle the expression for fg(x) 3x2 9x2 3x3 9x4
- November 2021, Paper 1H, Q24 (4 marks): (a) f(x) = cx + d f = 7 f = 22 Work out the values of c and d. c = d = 24 (b) g(x) = 2x and h(x) = 2 1 − x Circle the expression for hg(x) x x − 2 2 2 2 1 2 − x
- November 2020, Paper 3H, Q30 (4 marks): f(x) = 2 1 x g(x) = x – x2 Solve f –1(x) = gf(x) Answer
- November 2019, Paper 3H, Q17 (2 marks): f(x) = 3x2 – 4x + 8 for all values of x Jenny says, “f must equal 2 × f , because 10 is 2 × 5” Is Jenny correct? Show working to support your answer.
- November 2019, Paper 3H, Q28 (4 marks): f(x) = 2x – 3 and g(x) = x2 Show that f –1 = fg
- June 2019, Paper 1H, Q24 (1 mark): f(x) = sin(x – 90°) Circle the value of f(0°) 1 0 1 2 − –1
- June 2019, Paper 2H, Q27 (5 marks): f(x) = 5 2x – 1 Work out the value of f –1 + f(–0.5) Answer
- June 2019, Paper 3H, Q26 (3 marks): g(x) = 16 – x h(x) = x3 Solve gh(x) = 24 x =
- November 2018, Paper 2H, Q26 (3 marks): f(x) = 2 + x x g(x) = x2 – 2 Work out fg(x) Give your answer in the form a + bx n where a, b and n are integers. Answer
- November 2018, Paper 3H, Q26 (4 marks): f(x) = 4 3 2 − + x x Work out f –1(x) Answer
- June 2018, Paper 2H, Q28 (6 marks): f(x) = 5 – x and g(x) = 3x + 7 28 (a) Simplify f(2x) + g(x – 1) Answer 28 (b) Solve g–1(x) = 2x x =
- November 2017, Paper 3H, Q30 (2 marks): f(x) = 3 x + 4 for all values of x. g(x) = 6x2 + 3 for all values of x. Work out fg(x). Give your answer in the form ax2 + b where a and b are integers. Answer
- June 2017, Paper 2H, Q27 (4 marks): (a) h(x) = 3 x for all values of x On the grid, draw the graph of the inverse function y = h–1(x) for –2 ⩽ x ⩽ 2 27 (b) For all values of x f(x) = sin x g(x) =
- Specimen, Paper 1H, Q25 (3 marks): f(x) = 2x + c g(x) = cx + 5 fg(x) = 6x + d c and d are constants. Work out the value of d. Answer
- Specimen, Paper 2H, Q19 (1 mark): f(x) = 3x Circle the expression for f 1(x) – 3x x 3 x 3 1 3 x
- Specimen, Paper 3H, Q19 (4 marks): Here are two function machines, A and B. square add 6 Input Output A subtract 3 square Input Output B Both machines have the same input. Work out the range of i
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