plumiComposite and inverse functions: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.02.10 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 9 questions on Composite and inverse functions, as a list
- June 2025, Paper 3, Q4 (8 marks): Functions f and g are defined for all real values of x by x k - and ( )x 2 ( )x x kx , where k is a constant. f g 5 = = + + 2 1 ( )x kx You are given that the e
- June 2023, Paper 1, Q5 (8 marks): (a) The function ( )x f is defined for all values of x as ( ) f x ax b , where a and b are positive = - constants. (i) The graph of y f ( ) x + , where c is a c
- June 2022, Paper 2, Q6 (6 marks): (a) The diagrams show five different graphs. In each case the whole of the graph is shown. y y y x x x Fig. 1.1 Fig. 1.2 Fig. 1.3 y y x x Fig. 1.4 Fig. 1.5 Plac
- June 2022, Paper 3, Q2 (5 marks): x3 2 (a) Give full details of the single transformation that transforms the graph of y to the graph = 3 of y x - . 8 [2] = 3 The function f is defined by ( ) f
- November 2021, Paper 1, Q5 (7 marks): (a) The graph of the function y f ( ) x passes through the point P with coordinates (2, 6), and = is a one-one function. State the coordinates of the point corr
- November 2021, Paper 1, Q8 (10 marks): Functions f and g are defined for 0 x 2 by ( ) f x 2 tan x and ( ) g x sec x . G G = = r (a) (i) State the range of f. [1] (ii) State the range of g. [1] (b) (i
- November 2020, Paper 3, Q3 (11 marks): The functions f and g are defined for all real values of x by 2 f x ( ) 2 x 6 x and ( ) g x 3 x + . 2 = + = (a) Find the range of f. [3] (b) Give a reason why f
- June 2019, Paper 1, Q3 (7 marks): 3 The function f is defined by ( ) f x ( x 3 ) 17 for x k , where k is a constant. = - - H 1 (a) Given that f - ( )x exists, state the least possible value of k
- June 2018, Paper 3, Q4 (8 marks): In this question you must show detailed reasoning. The functions f and g are defined for all real values of x by ^ h ^ h x3 2 f x and g x x 2 . = = + (i) Write
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