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4MA1/1H Jun 2024, Question 15: Inverse Functions

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

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The question, in short

For f(x) = (3x + 1)/(x − 2), identify the excluded x value and find the inverse function f⁻¹(x).

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

Part (a) · 1 mark

State which value of x is excluded from the domain of f.

  1. 1The function is f(x) = (3x + 1)/(x − 2).
  2. 2The denominator cannot be zero, so x − 2 ≠ 0.
  3. 3Therefore, x ≠ 2.

Answer2

Part (b) · 3 marks

Find the inverse function and write it in the form f⁻¹(x) = ...

  1. 1Let y = (3x + 1)/(x − 2).
  2. 2Swap x and y: x = (3y + 1)/(y − 2).
  3. 3Multiply both sides by (y − 2): x(y − 2) = 3y + 1.
  4. 4Expand: xy − 2x = 3y + 1.
  5. 5Bring terms in y to one side: xy − 3y = 2x + 1.
  6. 6Factorise: y(x − 3) = 2x + 1.
  7. 7Solve for y: y = (2x + 1)/(x − 3).
  8. 8So f⁻¹(x) = (1 + 2x)/(x − 3).

Answer(1 + 2x)/(x − 3)

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