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4MA1/2H Nov 2021, Question 15: Inverse Functions

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 6 marks

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The question, in short

Given f(x) = 2x − 3 and g(x) = x/(3x + 1), identify an excluded x value for g, form the composite gf(x) in simplified form, and derive g⁻¹(x).

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Part (a) · 1 mark

Give the x value that g cannot accept.

  1. 1The denominator cannot be zero: 3x + 1 = 0
  2. 2x = −1/3

Answer−1/3

Part (b) · 2 marks

Work out gf(x) and simplify the result.

  1. 1gf(x) = g(2x − 3) = (2x − 3)/(3(2x − 3) + 1)
  2. 23(2x − 3) + 1 = 6x − 8
  3. 3gf(x) = (2x − 3)/(6x − 8)

Answer(2x − 3)/(6x − 8)

Part (c) · 3 marks

Write g⁻¹(x) as an expression in x.

  1. 1Let x = y/(3y + 1), so x(3y + 1) = y
  2. 23xy + x = y, so x = y − 3xy = y(1 − 3x)
  3. 3g⁻¹(x) = x/(1 − 3x)

Answerx/(1 − 3x)

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