Q. If $f:R \rightarrow R$ is defined as $f(x) = (1 - x)^{1/3}$, then $f^{- 1}(x)$ is
A) $(1 - x)^{- 1/3}$
B) $(1 - x)^{3}$
C) $1 - x^{3}$
D) $1 - x^{1/3}$
Explanation
(c)
Given, $f(x) = y = (1 - x)^{1/3}$
$\Rightarrow \ \ \ \ y^{3} = 1 - x$
$\Rightarrow \ \ \ \ \ \ x = 1 - y^{3}$
$\therefore\ \ \ f^{- 1}(x) = 1 - x^{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.