Q. If $f:R \rightarrow R$ defined by $f(x) = x^{3}$, then $f^{- 1}(8)$ is equal to
A) {2}
B) $\{ 2,\ \omega,\ 2\omega^{2}\}$
C) $\{ 2,\ - 2\}$
D) {2, 2}
Explanation
(a)
Let $y = f(x) = x^{3}$
$\therefore\ \ \ \ \ \ \ \ \ x = y^{1/3}$
$\Rightarrow \ \ \ \ \ \ \ \ f^{- 1}(x) = x^{1/3}$
$\therefore\ \ \ \ \ \ f^{- 1}(8) = (8)^{1/3} = 2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.