4MA1/1H Jan 2021, Question 22: Inverse Functions
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 3 marks
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The question, in short
Given f(x) = x² − 8x + 5 for x ≤ 4, find the inverse function f⁻¹(x) in the form f⁻¹(x) = ...
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Solution · 3 marks
- 1y = x² − 8x + 5
- 2x = y² − 8y + 5
- 3y² − 8y + 16 = x + 11
- 4(y − 4)² = x + 11
- 5y − 4 = ±sqrt(x + 11)
- 6y = 4 ± sqrt(x + 11)
- 7since x ≤ 4, take the negative root
- 8f⁻¹(x) = 4 − sqrt(x + 11)
Answer4 − √(x + 11)
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