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4024/11 Oct/Nov 2021, Question 21: Inverse Functions

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 7 marks

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The question, in short

For f(x) = 6/(2 − x), evaluate f(−1), find the inverse function f⁻¹(x), and solve f(t) = f(5t + 2) for t.

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Part (a) · 1 mark

Substitute x = −1 into f(x) = 6/(2 − x) and calculate the result.

  1. 1f(−1) = 6/(2 − (−1)) = 6/3 = 2

Answer2

Part (b) · 3 marks

Rearrange f(x) = 6/(2 − x) to express x in terms of the output, giving f⁻¹(x).

  1. 1y = 6/(2 − x), so 2 − x = 6/y
  2. 2x = 2 − 6/y
  3. 3f⁻¹(x) = 2 − 6/x

Answer2 − 6/x or (2x − 6)/x

Part (c) · 3 marks

Set f(t) equal to f(5t + 2) using the formula and solve for the value of t.

  1. 16/(2 − t) = 6/(2 − (5t + 2))
  2. 22 − t = 2 − 5t − 2 = −5t
  3. 34t = −2, t = −0.5

Answer−0.5 or −1/2

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Also searched as: 4024/11/O/N/21 · 4024_w21_qp_11 · 4024 w21 11 · question 21.
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