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4MA1/1H Jun 2021, Question 24: Inverse Functions

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 6 marks

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The question, in short

Given f(x) = 5x² − 10x + 7 for x ≥ 1 and g(x) = 7x − 6, find a composite value and derive the inverse of f.

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

Part (a) · 2 marks

Calculate fg(2), applying g first then f.

  1. 1g(2) = 7 × 2 − 6 = 8
  2. 2f(8) = 5(8)² − 10(8) + 7 = 5×64 − 80 + 7 = 320 − 80 + 7 = 247

Answer247

Part (b) · 4 marks

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

  1. 1Complete the square: f(x) = 5(x − 1)² + 2
  2. 2Write y = 5(x − 1)² + 2 and make x the subject
  3. 3y − 2 = 5(x − 1)², so (x − 1)² = (y − 2)/5
  4. 4x ≥ 1, so take the positive root: x = 1 + √((y − 2)/5)
  5. 5f⁻¹(x) = 1 + √((x − 2)/5)

Answer1 + √((x − 2)/5)

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