plumiFunctions, inverse and composite functions: Edexcel GCSE Maths questions
Every Edexcel 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 15 questions on Functions, inverse and composite functions, as a list
- June 2025, Paper 1H, Q17 (5 marks): g(x) = 1 – 3x h(x) = 2x 2 – 1 Show that 3gh(x) + hg(x) = 0 has just one solution for x.
- November 2024, Paper 1H, Q18 (4 marks): f ( ) x 4 –1 (x) (a) Find f f –1 (x) = For all values of x 2 and h(x) = 1 – 2x g(x) = (x – 1) (b) Work out the value of gh gh =
- June 2024, Paper 3H, Q16 (5 marks): The functions f and g are given by f(x) = 12 and g(x) = 5 – 3x x + 1 (a) Find f(–3) (b) Find fg –1 (c) Find g
- November 2023, Paper 2H, Q19 (4 marks): The functions f and g are such that f(x) = (2x + 3)2 and g(x) = 2x − 1 (a) Find gf(−3) (b) Find g−1(x) g−1(x) =
- June 2023, Paper 1H, Q20 (5 marks): For x 0, the functions f and g are such that x + 2 f (x) = 3x + 4 g(x) = 5 (a) Find g –1(x) – 1(x) = g (b) Solve gf (x) = 3 x =
- November 2022, Paper 2H, Q22 (3 marks): f(x) = x 3 g(x) = 2x + 3 h(x) = fg(x) Find h−1(x) h−1(x) =
- June 2022, Paper 2H, Q19 (4 marks): The functions g and h are such that h(x) = 1 g(x) = 3 2 x − 5 x (a) Find g (b) Find hg−1(x) Give your answer in terms of x in its simplest form. hg−1(x) =
- November 2021, Paper 1H, Q21 (6 marks): The functions f and g are such that f(x) = 3x2 + 1 for x > 0 and g(x) = 4 x for x > 0 2 (a) Work out gf The function h is such that h = (fg)–1 (b) Find h(x)
- November 2020, Paper 1H, Q19 (5 marks): f and g are functions such that 12 f(x) = x and g(x) = 3(2x + 1) (a) Find g (b) Find gf (c) Find g–1
- November 2019, Paper 1H, Q18 (6 marks): The function f is given by f(x) = 2x3 – 4 (a) Show that f –1 = 3 The functions g and h are given by g(x) = x + 2 and h(x) = x2 (b) Find the values of x for whic
- June 2019, Paper 1H, Q21 (7 marks): The functions f and g are such that f(x) = 3x – 1 and g(x) = x2 + 4 (a) Find f –1(x) f –1(x) = Given that fg(x) = 2gf(x), (b) show that 15x2 – 12x – 1 = 0
- November 2018, Paper 1H, Q19 (4 marks): For all values of x f(x) = (x + 1)2 and g(x) = 2(xí (a) Show that gf(x) = 2x(x + 2) (b) Find gí
- November 2018, Paper 3H, Q10 (4 marks): f(x VLQx° (a) Find f Give your answer correct to 3 significant figures. g(x) = 2x – 3 (b) Find fg Give your answer correct to 3 significant figures. h(x) =
- June 2018, Paper 2H, Q11 (3 marks): f and g are functions such that f(x) = 2 2x and g(x) = 4x3 (a) Find f(–5) (b) Find fg
- November 2017, Paper 2H, Q22 (5 marks): is 5 marks)
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