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WAEC Further Mathematics 2015 Question 10

Question 10

Functions

Given that f: x → (2x − 1)/(x + 2), x ≠ −2, find f−1, the inverse of f

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

Answer: A (f−1: x → (1 + 2x)/(2 − x), x ≠ 2)

Explanation

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