plumiComposite and inverse functions: Edexcel A‑Level Maths questions
Edexcel A-Level Maths past-paper questions on 2.10 Composite and inverse functions, 2010–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 11 questions on Composite and inverse functions, as a list
- June 2025, Pure 1, Q1 (4 marks): The point P(6, –4) lies on the curve with equation y = f(x), x ∈ Find the point to which P is mapped when the curve with equation y = f(x) is transformed to t
- June 2025, Pure 2, Q12 (8 marks): y x O Figure 3 Figure 3 shows a sketch of the graph with equation y = f (x) where f (x) = 4 ½x – 3½ – 5 x ∈ Given that a is a constant and ½a½ = 1 (a) find th
- June 2024, Pure 1, Q8 (11 marks): The functions f and g are defined by f(x) 2 4 3 5 9 , 2 9 2 x x x x x g(x) (a) Find fg(2) (2) (b) Find g –1 (3) (c) (i) Find gf(x), giving your answer as a simp
- June 2023, Pure 1, Q7 (8 marks): The function f is defined by f(x) = 3 + x −2 x ∈ x > 2 (a) State the range of f (1) (b) Find f –1 (3) The function g is defined by g(x) = 15 3 x − x ∈ x ≠ 3
- June 2022, Pure 2, Q10 (8 marks): The function f is defined by f(x) = 8 5 2 3 x x + + x > −3 2 (a) Find f −1 3 2 (2) (b) Show that f(x) = A + B x 2 3 + where A and B are constants to b
- November 2021, Pure 2, Q2 (5 marks): The functions f and g are defined by f (x) = 7 – 2x2 x Î g (x) = 3 5 1 x x − x Î x ≠1 5 (a) State the range of f (1) (b) Find gf (1.8) (2) (c) Find g–1(x) (
- November 2020, Pure 1, Q4 (5 marks): The function f is defined by f (x) = 3 7 2 x x − − x , x ≠ 2 (a) Find f −1(7) (2) (b) Show that ff (x) = ax b x + −3 where a and b are integers to be found.
- November 2020, Pure 1, Q9 (9 marks): y x O C Figure 2 Figure 2 shows a sketch of the curve C with equation y = f (x) where f (x) = 4(x2 − 2)e−2x x (a) Show that f ʹ(x) = 8(2 + x − x2)e−2x (3) (
- June 2019, Pure 1, Q5 (10 marks): f(x) = 2x2 + 4x + 9 x (a) Write f(x) in the form a(x + b)2 + c, where a, b and c are integers to be found. (3) (b) Sketch the curve with equation y = f(x) sho
- June 2019, Pure 2, Q6 (10 marks): y O x Figure 4 Figure 4 shows a sketch of the graph of y J [࣠) , where g( ) ( ) x x x x x = − + − ⎧ ⎨ ⎩ 2 1 4 7 2 2 2 - (a) Find the value of gg(0). (2) (b)
- June 2018, Pure 2, Q1 (6 marks): g(x) = 2 5 3 x x + − x 5 (a) Find gg(5). (2) (b) State the range of g. (1) (c) Find g−1(x), stating its domain. (3)
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