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4MA1/1HR Jan 2020, Question 17: Composite Functions

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 4 marks

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The question, in short

For f(x) = (x − 4)², evaluate f(1) and give the range of f; for g(x) = 4/(x + 3), x ≠ −3, work out fg(2).

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

Part (a) · 1 mark

Calculate f(1) using f(x) = (x − 4)².

  1. 1f(1) = (1 − 4)²
  2. 2(−3)² = 9

Answer9

Part (b) · 1 mark

State the range of the function f.

  1. 1(x − 4)² is a square, so it is never negative
  2. 2Its smallest value is 0, when x = 4, so f(x) ≥ 0

Answerf(x) ≥ 0

Part (c) · 2 marks

Work out fg(2) using g(x) = 4/(x + 3) and f(x) = (x − 4)².

  1. 1g(2) = 4 ÷ (2 + 3) = 0.8
  2. 2fg(2) = f(0.8) = (0.8 − 4)²
  3. 3(−3.2)² = 10.24 = 256/25

Answer256/25

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