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0580/42 Feb/Mar 2025, Question 14: Composite Functions

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 5 marks

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The question, in short

For f(x) = 5 − 4x, evaluate the function at a value, form a composite expression in x, and find the inverse function.

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

Part (a) · 1 mark

Calculate f(−3) using f(x) = 5 − 4x.

  1. 1f(−3) = 5 − 4 × (−3) = 5 + 12 = 17

Answer17

Part (b) · 2 marks

Substitute 3 − 2x into f and simplify the resulting expression.

  1. 1f(3 − 2x) = 5 − 4(3 − 2x)
  2. 2= 5 − 12 + 8x
  3. 3= 8x − 7

Answer8x − 7

Part (c) · 2 marks

Determine f⁻¹(x) for the function f(x) = 5 − 4x.

  1. 1y = 5 − 4x, swap: x = 5 − 4y
  2. 24y = 5 − x
  3. 3f⁻¹(x) = (5 − x)/4

Answer(5 − x)/4

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

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