plumiComposite and inverse functions: OCR MEI A‑Level Maths questions
OCR MEI 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 10 questions on Composite and inverse functions, as a list
- June 2025, Paper 3, Q2 (2 marks): You are given that 3 f x ( ) on the domain { : x x , x 0 } = d R ! x g x ( ) x - on the domain { : 1 x x } . = d R Find gf x . You must state the domain. ( ) [2
- June 2025, Paper 3, Q9 (5 marks): 3 x 9 The function ( ) f x is defined on all real numbers by ( ) f x x e . = + 3 3 x (a) Differentiate x e . [2] + (b) Write down the coordinates of the point w
- June 2024, Paper 3, Q2 (4 marks): (a) The function ( )x f is defined by 1 f ( )x 1 2 x for x H - . = + 2 1 Find an expression for f - ( )x and state the domain of this inverse function. [3] 2 (b
- June 2023, Paper 2, Q12 (4 marks): It is given that 1 • x x x f ( ) , 0 = 2 ! x • g ( ) x , x 3 = 2 x 3 - • 2 h ( ) x x 2 , x . = + ! R (a) Explain why f (x) is not a function. [1] (b) Find gh (x
- June 2022, Paper 3, Q2 (6 marks): The function ( ) f x x is defined on the domain x 0 . = H 2 The function ( ) g x 25 x is defined on the domain R. = - (a) Write down an expression for fg x . (
- June 2022, Paper 3, Q8 (16 marks): 3 8 The curves y h ( ) x and y h - ( ) x , where ( ) h x x - , are shown below. 8 = = = The curve y h ( ) x crosses the x-axis at B and the y-axis at A. = 1 The
- November 2020, Paper 2, Q15 (7 marks): Functions f (x) and g (x) are defined as follows. 3 f ( )x x for x 2 0 and ( )x g x - - for x 2 2. x 6 = = The function h (x) is defined as h (x) = fg (x). (a)
- June 2019, Paper 2, Q9 (9 marks): You are given that f ( ) x 2 x 3 for x 1 0 and = + + 2 g ( ) x x 2 x 1 for x 2 1 . = - (a) Find gf ( )x , stating the domain. [3] (b) State the range of gf ( )x
- June 2019, Paper 3, Q1 (6 marks): The function ( )x f is defined for all real x by f ( ) x 3 x 2 . = - 1 (a) Find an expression for f - ( )x . [2] 1 (b) Sketch the graphs of y f ( ) x and y f -
- June 2018, Paper 3, Q9 (4 marks): x e 9 The function ( )x is defined on the domain x x f , 0 . R ! = d x 1 e - f 1 (i) Find ( )x [3] - . f 1 (ii) Write down the range of ( )x [1] - . a 4
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