plumiComposite and inverse functions: AQA A‑Level Maths questions
AQA A-Level Maths past-paper questions on B.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 13 questions on Composite and inverse functions, as a list
- June 2025, Paper 1, Q12 (8 marks): Functions f and g are defined by f(x) = x2 + 5 x ∈ ℝ g(x) = √ x x ≥ 0 12 (a) Using set notation, state the range of f [2 marks] 12 (b) Determine whether f has a
- June 2024, Paper 1, Q2 (1 mark): The function f is defined by f (x) = ex + 1 for x ℝ Find an expression for f –1(x) Tick (✓) one box. [1 mark] f –1(x) = ln (x – 1) f –1(x) = ln (x) – 1 f –1(x)
- June 2024, Paper 1, Q17 (6 marks): The function f is defined by f (x) = | x | + 1 for x ℝ The function g is defined by g(x) = ln x where g has its greatest possible domain. 17 (a) Using set notat
- June 2023, Paper 2, Q7 (5 marks): The functions f and g are defined by f (x) = 10 − 2x p for x × 5 g(x) = 1 x for x 6= 0 The function h has maximum possible domain and is defined by h(x) = gf (x
- June 2022, Paper 3, Q3 (1 mark): The function f is defined by f (x) = 2x + 1 Solve the equation f (x) = f −1(x) Circle your answer. [1 mark] x = −1 x = 0 x = 1 x = 2
- June 2022, Paper 3, Q10 (13 marks): The function f is defined by f (x) = x2 + 10 2x + 5 where f has its maximum possible domain. The curve y = f (x) intersects the line y = x at the points P and Q
- November 2021, Paper 2, Q10 (11 marks): The function h is defined by h(x) = x p x − 3 where h has its maximum possible domain. 10 (a) Find the domain of h. Give your answer using set notation. [3 mark
- November 2020, Paper 1, Q13 (15 marks): The function f is defined by f (x) = 2x + 3 x × 2 x 2 R, x 6= 2 13 (a) (i) Find f ×1 [3 marks] 13 (a) (ii) Write down an expression for ff (x). [1 mark] 13 (b)
- November 2020, Paper 3, Q3 (1 mark): Determine which one of these graphs does not represent y as a function of x. Tick (3) one box. [1 mark] x y x y x y x y
- June 2019, Paper 1, Q6 (8 marks): The function f is defined by f (x) = 1 2 (x2 + 1), x × 0 6 (a) Find the range of f. [1 mark] 6 (b) (i) Find f −1(x) [3 marks] 6 (b) (ii) State the range of f −1
- June 2019, Paper 2, Q3 (1 mark): Each of these functions has domain x 2 R Which function does not have an inverse? Circle your answer. [1 mark] f (x) = x3 f (x) = 2x + 1 f (x) = x2 f (x) = ex f
- June 2018, Paper 1, Q4 (3 marks): The function f is defined by f (x) = e x−4, x 2 R Find f −1(x) and state its domain. [3 marks]
- June 2018, Paper 3, Q6 (13 marks): A function f is defined by f (x) = x 2x − 2 p 6 (a) State the maximum possible domain of f. [2 marks] 6 (b) Use the quotient rule to show that f 0(x) = x − 2 (2
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