Lemmara logoLemmaraWorked solution

0580/42 Feb/Mar 2022, Question 3: Composite Functions

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 6 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

For f(x) = 1 + 4x and g(x) = x², evaluate a composite at 3, form a composite function, simplify an inverse composition, and solve f(x) = 15.

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

Part (ai) · 2 marks

Calculate gf(3), working out g of f of 3.

  1. 1f(3) = 1 + 4 × 3 = 13
  2. 2gf(3) = g(13) = 13² = 169

Answer169

Part (aii) · 1 mark

Find fg(x) as an expression in x.

  1. 1fg(x) = f(x²) = 1 + 4x²

Answer1 + 4x²

Part (aiii) · 1 mark

Find f⁻¹f(x), simplifying fully.

  1. 1f⁻¹ undoes f, so f⁻¹f(x) = x

Answerx

Part (b) · 2 marks

Find the value of x for which f(x) = 15.

  1. 11 + 4x = 15
  2. 24x = 14, x = 3.5

Answer3.5 or 7/2

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

Practise more composite functions questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on composite functions

Also searched as: 0580/42/F/M/22 · 0580_m22_qp_42 · 0580 m22 42 · question 3.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.