Lemmara logoLemmaraWorked solution

4024/22 Oct/Nov 2023, Question 11: Composite Functions

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 6 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Given f(x) = 4x + 1 and g(x) = 2x − 3, evaluate f(−3), find the inverse of g, and combine two reciprocal expressions into one simplified fraction.

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

Part (a) · 1 mark

Work out the value of f(−3) using f(x) = 4x + 1.

  1. 1f(−3) = 4 × (−3) + 1 = −11

Answer−11

Part (b) · 2 marks

Find g⁻¹(x), the inverse function of g(x) = 2x − 3.

  1. 1y = 2x − 3 so x = 2y − 3 (swap)
  2. 2y = (x + 3)/2
  3. 3g⁻¹(x) = (x + 3)/2

Answer(x +3)/2

Part (c) · 3 marks

Simplify 2/f(x) + 1/g(x) into a single fraction in x, fully simplified.

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

Answer(8x −5)/((4x +1)(2x −3)) or (8x−5)/(8x²−10x−3)

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

Practise more composite functions questions

Real 4024 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: 4024/22/O/N/23 · 4024_w23_qp_22 · 4024 w23 22 · question 11.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.