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4MA1/1H Jun 2022, Question 14: Inverse Functions

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

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The question, in short

Evaluate a rational function at x = 10, then rearrange to find its inverse function, stating it in the form f⁻¹ : x ↦ …

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

Part (a) · 1 mark

Substitute 10 into 2x/(x − 6) and work out the resulting value.

  1. 1f(10) = 2 × 10 / (10 − 6)
  2. 2f(10) = 20 / 4
  3. 3f(10) = 5

Answer5

Part (b) · 3 marks

Rearrange y = 2x/(x − 6) to make x the subject, giving the inverse as a function of x.

  1. 1Let y = f(x) = 2x / (x − 6)
  2. 2y(x − 6) = 2x
  3. 3yx − 6y = 2x
  4. 4yx − 2x = 6y
  5. 5x(y − 2) = 6y
  6. 6x = 6y / (y − 2)
  7. 7f⁻¹(x) = 6x / (x − 2)

Answer6x / (x − 2)

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