Q. Which of the following functions is inverse of itself?
A) $f(x) = \frac{1 - x}{1 + x}$
B) $f(x) = 3^{\log x}$
C) $f(x) = 3^{x(x + 1)}$
D) None of these
Explanation
(a)
$fof = \frac{1 - f(x)}{1 + f(x)} = \frac{1 - \frac{1 - x}{1 + x}}{1 + \frac{1 - x}{1 + x}}$
$\Rightarrow \ \ \ \ \ \ \ \ \ f\left\lbrack f(x) \right\rbrack = x$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ f(x) = f^{- 1}(x)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.