4MA1/2HR Jan 2022, Question 23: Composite Functions
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks
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The question, in short
Find the inverse of the composite function h(x) = fg(x) with f(x) = x + 25, g(x) = x² − 12x, and domain x ≤ 6.
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Solution · 4 marks
- 1h(x) = f(x² − 12x) = x² − 12x + 25
- 2Complete the square: h(x) = (x − 6)² − 11
- 3Let y = (x − 6)² − 11, so x − 6 = ±√(y + 11)
- 4Domain x ≤ 6 needs the negative root: x = 6 − √(y + 11)
- 5h⁻¹(x) = 6 − √(11 + x)
Answer6 − √(11 + x)
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