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4MA1/1HR Jun 2020, Question 16: Composite Functions

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 9 marks

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The question, in short

Given f(x) = 5x − 7 and g(x) = 5x/(x + 4), find an excluded domain value, a composite value, solve a composite equation, and find the inverse of g.

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

Part (a) · 1 mark

State the value of x that cannot be in the domain of g.

  1. 1g(x) = 5x / (x + 4)
  2. 2The denominator cannot be zero, so x + 4 ≠ 0
  3. 3x ≠ −4

Answer−4

Part (b) · 2 marks

Calculate gf(2.6), applying f first then g.

  1. 1f(2.6) = 5 × 2.6 − 7 = 13 − 7 = 6
  2. 2g(6) = (5 × 6) / (6 + 4) = 30 / 10 = 3

Answer3

Part (c) · 3 marks

Solve fg(x) = 2 for x.

  1. 1fg(x) = 5 × (5x / (x + 4)) − 7 = 2
  2. 2(25x / (x + 4)) − 7 = 2
  3. 325x / (x + 4) = 9
  4. 425x = 9(x + 4)
  5. 525x = 9x + 36
  6. 616x = 36
  7. 7x = 36 / 16 = 2.25

Answer2.25

Part (d) · 3 marks

Find g⁻¹ and express it in the form g⁻¹ : x ↦ ...

  1. 1Let y = g⁻¹(x), so x = 5y / (y + 4)
  2. 2x(y + 4) = 5y
  3. 3xy + 4x = 5y
  4. 44x = 5y − xy
  5. 54x = y(5 − x)
  6. 6y = 4x / (5 − x)

Answer4x / (5 − x)

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