plumiComposite and inverse functions: WJEC A‑Level Maths questions
WJEC A-Level Maths past-paper questions on 2.10 Composite and inverse functions, 2018–2025, 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 6 questions on Composite and inverse functions, as a list
- Summer 2025, Unit 3, Q15 (7 marks): f x , where x ` 3. 15. A function f is defined by 2 x 3 (a) Determine the range of f. [2] f 1( ) x (b) Find an expression for . [5]
- Summer 2024, Unit 3, Q10 (14 marks): 10. The function f has domain 4, and is defined by 2 3 x 1 x f x . x 1 2 x 2 x 3 2 x f x (a) Show that . [4] x 3 Determine the
- Summer 2023, Unit 3, Q10 (8 marks): 0 Two real functions are defined as 8 ( ) = f x 4 4 for x x , x − 4 ( ) = x − 2 ( )2 g x x for . ( ). Find an expression for fg x a)
- Summer 2022, Unit 3, Q12 (13 marks): 2 The diagram below shows a sketch of the graph of y = f (x), where ( ) = 2x2 +12x +10. f x The graph intersects the x-axis at the points (p, 0), (q, 0) and the
- Summer 2019, Unit 3, Q11 (7 marks): 1 The function f (x) is defined by x2 −1 ( ) = f x x with domain x x 1. Find an expression for f –1(x). State the domain for f –1 and sketch both f (x) and a) f
- Summer 2018, Unit 3, Q12 (10 marks): Given that f is a function, 1 2 a) state the condition for f –1 to exist, i) find ff –1(x). ii) [2] The functions g and h, are given by b) g(x) = x2 – 1, h(x) =
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