Lemmara logoLemmaraWorked solution

4MA1/2H Jan 2019, Question 17: Composite Functions

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 4 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Given f(x) = 4 − 3x and g(x) = 1/(1 − 2x), evaluate f at 5, find the excluded x for g, and work out the composite fg at −1.5.

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

Part (a) · 1 mark

Substitute x = 5 into f(x) = 4 − 3x and calculate the result.

  1. 1f(5) = 4 − 3 × 5
  2. 24 − 15 = −11

Answer−11

Part (b) · 1 mark

State the value of x for which g(x) = 1/(1 − 2x) is undefined.

  1. 1g(x) = 1 / (1 − 2x)
  2. 2Denominator cannot be zero, so 1 − 2x ≠ 0
  3. 32x = 1
  4. 4x = 0.5

Answer0.5

Part (c) · 2 marks

Work out fg(−1.5), applying g first then f to the result.

  1. 1g(−1.5) = 1 / (1 − 2 × −1.5)
  2. 2g(−1.5) = 1 / (1 + 3)
  3. 3g(−1.5) = 1 / 4 = 0.25
  4. 4f(g(−1.5)) = f(0.25)
  5. 5f(0.25) = 4 − 3 × 0.25
  6. 64 − 0.75 = 3.25

Answer3.25

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

Practise more composite functions questions

Real 4MA1 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: 4MA1 2H January 2019 · 4MA1/2H · 4ma1 jan19 2h · question 17.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.