Function notation: Edexcel International GCSE Maths questions

Every Edexcel International GCSE Maths exam question on 3.2 Function notation, 2019–2025, with its mark scheme and examiner’s report.

All 46 questions on Function notation, as a list

June 2025 (R), Paper 1 Higher, Q21 (3 marks): The curve with equation y = f(x) has one turning point. The coordinates of this turning point are (−6, 9) (a) Write down the coordinates of the turning point on
June 2025 (R), Paper 2 Higher, Q19 (3 marks): The functions f and g are such that x x 4 where x > 2 f( ) 3 x g( ) x x 2 1 (a) State the value of x that cannot be included in any domain of g (b) Find gf(x) G
June 2025, Paper 1 Higher, Q16 (4 marks): f (x) = 9 – x where x  0 2 g (x) = 4x (a) Find f (b) Solve fg (x) < 0 Show clear algebraic working.
June 2025, Paper 1 Higher, Q19 (2 marks): The equation of a curve is y = f (x) There is only one minimum point on the curve. The coordinates of this minimum point are (8, –12) Write down the coordinates
November 2024, Paper 1 Higher, Q25 (4 marks): The function f is such that f x where x  6 x x 2 2 24 7 Find the inverse function f 1 x f 1 x
November 2024, Paper 2 Higher, Q19 (3 marks): A curve has equation y f x There is only one minimum point on the curve. The coordinates of this minimum point are (5, 4) Write down the coordinates of the mini
June 2024 (R), Paper 2 Higher, Q17 (3 marks): f( ) x g( ) x 3 x 1 x 2 4 Given that fg(k) = 2 work out the value of k k =
June 2024 (R), Paper 2 Higher, Q23 (2 marks): A curve has equation y = f(x) The coordinates of the minimum point on this curve are (6, −3) Write down the coordinates of the minimum point on the curve with e
June 2024, Paper 1 Higher, Q15 (4 marks): The function f is defined as x f : x  3 1 x 2 (a) State the value of x that cannot be included in any domain of the function f –1 in the form f –1(x) = ... (b)
June 2024, Paper 1 Higher, Q21 (2 marks): A curve has equation y = f (x) There is one minimum point on this curve. The coordinates of this minimum point are (5, ‒4) Write down the coordinates of the min
November 2023, Paper 1 Higher, Q24 (4 marks): The curve with equation f(x) = 5 is transformed to the curve with equation x 2 + x + 9 2 by the translation a 2 g(x) = 5 x 4 9 x 4 8 b (a) Write down the val
November 2023, Paper 2 Higher, Q19 (7 marks): The functions f and g are such that x x  f : 5 7 5 x  g : x 2 9 (a) State which value of x cannot be included in any domain of g (b) Find fg The function h is
June 2023 (R), Paper 1 Higher, Q20 (7 marks): Curve C has equation y = f (x) The graph of curve C has one maximum point. The coordinates of this maximum point are (3, 5) (a) Write down the coordinates of th
June 2023, Paper 1 Higher, Q17 (4 marks): The functions g and h are such that 11 g(x) = 2 x − 5 h(x) = x 2 + 4 x  0 (a) What value of x must be excluded from any domain of g? (b) Solve gh(x) = 1
June 2023, Paper 1 Higher, Q21 (2 marks): A curve has equation y = f(x) There is only one turning point on the curve. The coordinates of this turning point are (6, 5) Write down the coordinates of the t
January 2023 (R), Paper 1 Higher, Q16 (6 marks): The function f is such that 2 where x ≠ 5 f(x) = 3 x − 5 3 (a) Find f 1     3 (b) Find f –1(x) f –1(x) = The function g is such that g(x) = 5x2 – 20x + 23
January 2023, Paper 1 Higher, Q18 (4 marks): The function f is such that f(x) = k x where x ≠ 0 and k is an integer. (a) Express the inverse function f −1 in the form f−1(x) = ... f−1(x) = The function g i
January 2023, Paper 2 Higher, Q25 (4 marks): The function f is such that f(x) = 3x2 – 12x + 7 where x  2 Express the inverse function f –1 in the form f –1(x) = … f –1(x) =
June 2022 (R), Paper 2 Higher, Q19 (4 marks): f(x) = x 2 – 4 g(x) = 2x + 1 Solve fg(x) > 0 Show clear algebraic working.
June 2022 (R), Paper 2 Higher, Q22 (4 marks): The point A with coordinates (–3, 2) lies on the straight line with equation y = f(x) (a) Find the coordinates of the image of the point A on the straight line
June 2022, Paper 1 Higher, Q14 (4 marks): The function f is defined as x f : x  2 x ≠ 6 x − 6 (a) Find f (b) Express the inverse function f−1 in the form f−1 : x  … f−1 : x 
June 2022, Paper 1 Higher, Q20 (2 marks): The diagram shows a sketch of part of the curve with equation y = f (x) y (s, t) y = f (x) O x There is one maximum point on this curve. The coordinates of this
January 2022 (R), Paper 1 Higher, Q20 (6 marks): The curve with equation y = f(x) has one turning point. The coordinates of this turning point are (– 6, – 4) (a) Write down the coordinates of the turning point
January 2022 (R), Paper 2 Higher, Q23 (4 marks): The functions f and g are such that f(x) = x + 25 g(x) = x2 – 12x The function h is such that h(x) = fg(x) The domain of h is {x : x  6} Express the inverse fu
January 2022, Paper 1 Higher, Q23 (2 marks): The diagram shows a sketch of the curve with equation y = f(x) y (5, 7) y = f(x) O x There is only one maximum point on the curve. The coordinates of this maxim
January 2022, Paper 2 Higher, Q25 (5 marks): The function g is defined as g : x  5 + 6x − x2 with domain {x : x  3} (a) Express the inverse function g−1 in the form g−1 : x  … g−1 : x  (b) State the do
November 2021, Paper 2 Higher, Q15 (6 marks): The functions f and g are such that f ( ) x = 2 x - 3 x g ( ) x = 3 x 1 + (a) State the value of x that cannot be included in any domain of g (b) Find gf(x) Sim
June 2021, Paper 1 Higher, Q24 (6 marks): The functions f and g are defined as f(x) = 5x2 − 10x + 7 where x  1 g(x) = 7x − 6 (a) Find fg (b) Express the inverse function f −1 in the form f −1 (x) = ...
January 2021 (R), Paper 2 Higher, Q17 (9 marks): The functions f and g are defined as f(x) = x 2 + 6 g(x) = x – 10 (a) Find fg (b) Solve the equation fg(x) = f(x) Show clear algebraic working. The function h i
January 2021, Paper 1 Higher, Q21 (4 marks): A curve has equation y = f(x) The coordinates of the minimum point on this curve are (–9, 15) (a) Write down the coordinates of the minimum point on the curve w
January 2021, Paper 1 Higher, Q22 (3 marks): The function f is such that f(x) = x 2 – 8x + 5 where x  4 –1 in the form f –1(x) = ... Express the inverse function f f –1(x) =
November 2020 (R), Paper 1 Higher, Q16 (9 marks): The functions f and g are defined as f : x  5x – 7 5 x g : x  x + 4 (a) Write down the value of x that must be excluded from any domain of g (b) Find gf(2.6)
November 2020 (R), Paper 1 Higher, Q20 (2 marks): A curve has equation y = f(x) There is only one maximum point on the curve. The coordinates of this maximum point are (–3, 4) Write down the coordinates of the
November 2020, Paper 1 Higher, Q25 (3 marks): The curve with equation y = g(x) is transformed to the curve with equation y = −g(x) by the single transformation T. (a) Describe fully the transformation T. Th
November 2020, Paper 2 Higher, Q21 (7 marks): The function f is such that f(x) = 5 + 6x – x2 for x  3 (a) Express 5 + 6x – x2 in the form p – (x – q)2 where p and q are constants. (b) Using your answer to
January 2020 (R), Paper 1 Higher, Q17 (4 marks): The function f is such that f (x) = (x − 4)2 for all values of x. (a) Find f (b) State the range of the function f. 4 The function g is such that g(x) = x ≠ −3
January 2020 (R), Paper 1 Higher, Q22 (4 marks): The graph of y = a cos(x + b)° for 0  x  360 is drawn on the grid. y 3 2 1 O x 60 120 180 240 300 360 −1 −2 −3 (a) Find the value of a and the value of b. a =
January 2020, Paper 1 Higher, Q21 (5 marks): The functions f and g are such that f(x) = x2 − 2x g(x) = x + 3 The function h is such that h(x) = fg(x) for x  −2 Express the inverse function h−1(x) in the f
January 2020, Paper 2 Higher, Q21 (4 marks): The diagram shows a sketch of part of the curve with equation y = f(x) y (4, 6) y = f(x) O x There is one maximum point on this curve. The coordinates of this m
June 2019 (R), Paper 1 Higher, Q21 (4 marks): A curve has equation y = f(x) There is only one maximum point on the curve. The coordinates of this maximum point are (4, 3) (a) Write down the coordinates of t
June 2019 (R), Paper 2 Higher, Q18 (9 marks): The functions f and g are defined as x f(x) = and g(x) = xí 4 x 3 − (a) State which value of x must be excluded from any domain of the function f. (b) Find f
June 2019, Paper 2 Higher, Q24 (5 marks): The function f is such that f (x) = 3x – 2 (a) Find f The function g is such that g(x) = 2x2 – 20x + 9 where x . 5 (b) Express the inverse function g–1 in the f
January 2019 (R), Paper 1 Higher, Q23 (6 marks): The function f is defined as f(x) = for x > 0 and where k is a positive number. x (a) Find the value of p for which f −1(p) = k p = The function g is defined as
January 2019, Paper 1 Higher, Q18 (3 marks): The graph of y = f(x) is shown on the grid. y 4 2 O −8 −6 −4 −2 2 4 6 8 x −2 −4 −6 −8 1   (a) On the grid above, sketch the graph of y = f x   2 The graph
January 2019, Paper 1 Higher, Q19 (5 marks): g is the function with domain x  –3 such that g(x) = x2 + 6x (a) Write down the range of g–1 (b) Express the inverse function g–1 in the form g–1 : x g–1 : x
January 2019, Paper 2 Higher, Q17 (4 marks): f is the function such that f(x) = 4 – 3x (a) Work out f 1 g is the function such that g( ) x = 1 2 − x (b) Find the value of x that cannot be included in any d

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