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4024/23 May/Jun 2025, Question 10: Functions as a Mapping

Cambridge O Level Mathematics 4024 · Paper 23 (Calculator) · Calculator · 7 marks

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The question, in short

Given f(x) = 3x − 5 and g(x) = 2 − 6x, evaluate, solve and compose these functions, and find the range of g for x > −8.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 1 mark

Find f(2).

  1. 1f(2) = 3 × 2 − 5 = 1

Answer1

Part (b) · 2 marks

Solve g(x) = 18 for x.

  1. 12 − 6x = 18
  2. 2−6x = 16
  3. 3x = −16/6 = −8/3

Answer−8/3

Part (c) · 2 marks

Find fg(4), the composite function applied at 4.

  1. 1g(4) = 2 − 6 × 4 = −22
  2. 2fg(4) = f(−22) = 3 × (−22) − 5 = −71

Answer−71

Part (d) · 2 marks

Given the domain x > −8, find the range of g(x).

  1. 1g(−8) = 2 − 6 × (−8) = 50
  2. 2g decreases as x increases, so for x > −8, g(x) < 50

Answerg(x) < 50

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