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WAEC Further Mathematics 2024 Question 10

Question 10

Functions

If f(x) = (2 − x)/x, x ≠ 0, find the inverse of f.

  1. A.2/(x − 1), x ≠ 1
  2. B.2/(x + 1), x ≠ −1
  3. C.2/(1 − x), x ≠ 1
  4. D.2/(2 + x), x ≠ −2
Show the answer and explanation

Answer: B (2/(x + 1), x ≠ −1)

Explanation

y = (2 − x)/x gives xy = 2 − x, x(y + 1) = 2, x = 2/(y + 1). So f⁻¹(x) = 2/(x + 1), x ≠ −1.