Allied & ICAR Exam Bank • ALLIED_1723 MCQ • 2 Marks

Section 8: General Aptitude

Quantitative Aptitude

Subtopic: Numerical Computation

Question Statement:

If $f(x) = \frac{x - 1}{x + 1}$ for $x \neq -1$, then the inverse function $f^{-1}(x)$ is:

Options:

  • (A) $\frac{1 + x}{1 - x}$
  • (B) $\frac{1 - x}{1 + x}$
  • (C) $\frac{x + 1}{x - 1}$
  • (D) $\frac{x - 1}{1 + x}$

Answer Key:

A

Step-by-Step Solution & Explanation

$y = \frac{x - 1}{x + 1} \implies y(x + 1) = x - 1 \implies yx + y = x - 1 \implies x(1 - y) = 1 + y \implies x = \frac{1 + y}{1 - y}$.
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