Question

If $f:R\to R$ such that $f\left(x\right)=lo{g}_{3}x$ then $f^{-1}x$ is equal to

• A. $log{x}^3$
• B. $3^x$
• C. $3^{-x}$
• D. $3^{1/x}$

Answer 1

The correct option is B $3^x$

$f\left(x\right)$ is invertible for all positive $x$.

$y=lo{g}_3\left(x\right)$

Taking antilogarithm on both sides, we get

$3^y=x$.

Hence,

$f^{-1}\left(x\right)=3^x$

Hence, option 'B' is correct.