0580/23 May/Jun 2023, Question 20: Composite Functions

Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Calculator · 6 marks

The question, in short

Given f(x) = 6x − 7 and g(x) = x⁻³, find a simplified expression for f(x + 2), the inverse function f⁻¹(x), and the value of x satisfying g(x) = f(22).

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

Part (a) · 2 marks

Substitute x + 2 into f and simplify the resulting expression.

1f(x + 2) = 6(x + 2) − 7
2= 6x + 12 − 7
3= 6x + 5

Answer6x + 5

Part (b) · 2 marks

Find the inverse function f⁻¹(x).

1y = 6x − 7, swap: x = 6y − 7
26y = x + 7
3f⁻¹(x) = (x + 7)/6

Answer(x + 7)/6 or x/6 + 7/6

Part (c) · 2 marks

Find x when g(x) equals f(22).

1f(22) = 6 × 22 − 7 = 125
2x⁻³ = 125, so x³ = 1/125
3x = 1/5 = 0.2

Answer1/5 or 0.2

Stuck on a step? Read the free lesson: Composite Functions

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