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4MA1/2H Jun 2019, Question 24: Inverse Functions

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 5 marks

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The question, in short

For f(x) = 3x − 2 find f(5), and for g(x) = 2x² − 20x + 9 with x ≥ 5 find the inverse function g⁻¹(x).

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Part (a) · 1 mark

Calculate the value of f(5) using f(x) = 3x − 2.

  1. 1f(5) = 3(5) − 2 = 15 − 2 = 13

Answer13

Part (b) · 4 marks

Find g⁻¹(x) for g(x) = 2x² − 20x + 9, x ≥ 5, giving it in the form g⁻¹(x) = ...

  1. 1Complete the square: y = 2(x − 5)² − 50 + 9 = 2(x − 5)² − 41
  2. 2(x − 5)² = (y + 41)/2
  3. 3x ≥ 5, so x = 5 + √((y + 41)/2)
  4. 4Swap x and y: g⁻¹(x) = 5 + √((x + 41)/2)

Answerg⁻¹(x) = 5 + √((x + 41)/2)

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