0580/21 Oct/Nov 2025, Question 18: Composite Functions
Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Non-calculator · 4 marks
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The question, in short
Use f(x) = 2x + 5 to expand f(x)f(x) − ff(x) and find the coefficients a, b and c of ax² + bx + c.
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Solution · 4 marks
- 1f(x)f(x) = (2x + 5)² = 4x² + 10x + 10x + 25 = 4x² + 20x + 25
- 2ff(x) = 2(2x + 5) + 5 = 4x + 15
- 3f(x)f(x) − ff(x) = 4x² + 20x + 25 − 4x − 15 = 4x² + 16x + 10
- 4a = 4, b = 16, c = 10
Answera = 4, b = 16, c = 10
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Also searched as: 0580/21/O/N/25 · 0580_w25_qp_21 · 0580 w25 21 · question 18.
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