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4MA1/1H Jun 2023, Question 17: Composite Functions

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

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The question, in short

Given g(x) = 11/(2x − 5) and h(x) = x² + 4 for x ≥ 0, find an excluded domain value for g and solve the composite equation gh(x) = 1.

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Part (a) · 1 mark

State which value of x cannot be used in the domain of g.

  1. 1g(x) = 11 / (2x − 5)
  2. 2A fraction has no value when its denominator is 0
  3. 32x − 5 = 0
  4. 42x = 5
  5. 5x = 2.5

Answer2.5

Part (b) · 3 marks

Solve gh(x) = 1, giving the value(s) of x.

  1. 1gh(x) = g(x² + 4) = 11/(2(x² + 4) − 5) = 11/(2x² + 3)
  2. 2Set equal to 1: 2x² + 3 = 11, so x² = 4
  3. 3x = ±2, but x ≥ 0
  4. 4x = 2

Answer2

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