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4MA1/1H Jun 2018, Question 14: Inverse Functions

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 7 marks

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The question, in short

For f(x) = (3x − 5)/4 and g(x) = √(19 − x), evaluate f at −7, find the inverse of f, compute fg(3), and identify x values excluded from any domain of g.

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

Part (a) · 1 mark

Calculate f(−7) using f(x) = (3x − 5)/4.

  1. 1f(−7) = (3 × (−7) − 5) / 4
  2. 23 × (−7) − 5 = −21 − 5 = −26
  3. 3−26 / 4 = −6.5

Answer−6.5

Part (b) · 2 marks

Find f⁻¹(x) in the form f⁻¹(x) = ... by rearranging f.

  1. 1Write y = (3x − 5)/4
  2. 2Multiply both sides by 4: 4y = 3x − 5
  3. 3Add 5, then divide by 3: x = (4y + 5)/3
  4. 4Swapping the letters back, f⁻¹(x) = (4x + 5)/3

Answer(4x + 5)/3

Part (c) · 2 marks

Find fg(3), applying g then f, with g(x) = √(19 − x).

  1. 1g(3) = √(19 − 3) = √16 = 4
  2. 2fg(3) = f(4) = (3 × 4 − 5) / 4
  3. 33 × 4 − 5 = 7, so fg(3) = 7/4 = 1.75

Answer1.75

Part (d) · 2 marks

State which x values cannot belong to any domain of g(x) = √(19 − x).

  1. 1g(x) = √(19 − x), and a square root needs 19 − x ≥ 0
  2. 219 − x ≥ 0 gives x ≤ 19
  3. 3So no domain of g can contain x > 19

Answerx > 19

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