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4024/22 May/Jun 2021, Question 8: Functions as a Mapping

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 8 marks

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The question, in short

Given f(x) = 3x − 5 and g(x) = (4x + 4)/3, evaluate, solve inequalities and equations, and work with the inverse of g.

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

Part (a) · 1 mark

Find the value of f(−2).

  1. 1f(−2) = 3 × (−2) − 5
  2. 2= −11

Answer−11

Part (b) · 3 marks

Find the largest integer x for which f(x) > 3g(x).

  1. 13x − 5 > 3 × (4x + 4)/3
  2. 23x − 5 > 4x + 4
  3. 3x < −9
  4. 4Largest integer x = −10

Answer−10

Part (c) · 3 marks

Solve f(x) = g(3x − 5) for x.

  1. 1g(3x − 5) = (4(3x − 5) + 4)/3 = (12x − 16)/3
  2. 23(3x − 5) = 12x − 16
  3. 39x − 15 = 12x − 16 → 3x = 1
  4. 4x = 1/3

Answer1/3 or 0.3333…

Part (d) · 1 mark

Solve g⁻¹(x) = 5 for x.

  1. 1g⁻¹(x) = 5 means x = g(5)
  2. 2x = (4 × 5 + 4)/3 = 8

Answer8

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Also searched as: 4024/22/M/J/21 · 4024_s21_qp_22 · 4024 s21 22 · question 8.
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