Q. If $f(x) = \frac{2x - 1}{x + 5}(x \neq - 5)$, then $f^{- 1}(x)$ is equal to
A) $\frac{x + 5}{2x - 1},\ x \neq \frac{1}{2}$
B) $\frac{5x + 1}{2 - x},\ x \neq 2$
C) $\frac{x - 5}{2x + 1},\ x \neq \frac{1}{2}$
D) $\frac{5x - 1}{2 - x},\ x \neq 2$
Explanation
(b)
Let $y = \frac{2x - 1}{x + 5}$
$\Rightarrow \ \ \ \ \ \ \ \ \ x = \frac{5y + 1}{2 - y}$
$\therefore f^{- 1}(x) = \frac{5x + 1}{2 - x},\ x \neq 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.