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WAEC Further Mathematics 2008 Question 3

Question 3

Functions

A function f is defined on R, the set of real numbers, by f : x → (x + 3)/(x − 1), x ≠ 2. Find f−1

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

Answer: B (f−1 : x → (x + 3)/(x − 1), x ≠ −2)

Explanation

Let y = (x + 3)/(x − 1). Then yx − y = x + 3, so x(y − 1) = y + 3 and x = (y + 3)/(y − 1). The inverse has the same rule as f.