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4MA1/1H Jan 2019, Question 19: Inverse Functions

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks

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The question, in short

For g(x) = x² + 6x with domain x ≥ −3, state the range of the inverse and find an expression for g⁻¹(x).

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

Part (a) · 1 mark

State the range of g⁻¹.

  1. 1The range of g⁻¹ is the same as the domain of g
  2. 2Domain of g is x ≥ −3, so the range of g⁻¹ is y ≥ −3

Answery ≥ −3

Part (b) · 4 marks

Find g⁻¹(x) as an expression in x, written in mapping form.

  1. 1Let y = x² + 6x and complete the square: y = (x + 3)² − 9
  2. 2(x + 3)² = y + 9, so x + 3 = √(y + 9) (positive root, as x ≥ −3)
  3. 3x = −3 + √(y + 9)
  4. 4Swap x and y: g⁻¹ : x ↦ −3 + √(x + 9)

Answerg⁻¹ : x ↦ −3 + √(x + 9)

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