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JAMB Mathematics 1983 Question 40

Question 40

Algebraic Expressions

If f(x) = 1/(x − 1) + (x − 1)/(x2 − 1), find f(1 − x)

  1. A.1/x + 1/(x − 2)
  2. B.x + 1/(2x − 1)
  3. C.−1/x − 1/(x − 2)
  4. D.−1/x − 1/(2x − 1)
  5. E.1/x + 1/(x2 − 1)
Show the answer and explanation

Answer: C (−1/x − 1/(x − 2))

Explanation

f(x) simplifies to 1/(x − 1) + 1/(x + 1). Replacing x by 1 − x gives 1/(−x) + 1/(2 − x) = −1/x − 1/(x − 2).