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4024/21 May/Jun 2021, Question 6: Functions as a Mapping

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 10 marks

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The question, in short

Given f(x) = 2x + 3 and g(x) = (12 − 3x)/5, evaluate g(−1), solve f(x) = 2, find g⁻¹(x), and find x where f(x) exceeds g(x) by 4.

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Part (a) · 1 mark

Calculate the value of g(−1).

  1. 1g(−1) = (12 − 3 × (−1))/5
  2. 2= 15/5 = 3

Answer3

Part (b) · 2 marks

Solve the equation f(x) = 2 for x.

  1. 12x + 3 = 2
  2. 22x = −1
  3. 3x = −1/2

Answer−1/2 or −0.5

Part (c) · 3 marks

Determine the inverse function g⁻¹(x).

  1. 1y = (12 − 3x)/5
  2. 2Swap: x = (12 − 3y)/5
  3. 35x = 12 − 3y
  4. 43y = 12 − 5x
  5. 5g⁻¹(x) = (12 − 5x)/3

Answer(12 − 5x)/3 or 4 − 5/3 x

Part (d) · 4 marks

Find x such that f(x) is 4 more than g(x).

  1. 12x + 3 = (12 − 3x)/5 + 4
  2. 2Multiply by 5: 10x + 15 = 12 − 3x + 20
  3. 313x = 17
  4. 4x = 17/13

Answer17/13 or 1 4/13

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