Question

If $f:R^{+}\to R$ such that $f\left(x\right)={\log }_{3}x$ then $f^{-1}\left(x\right)=$

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

Answer 1

The correct option is B $3^x$

Let $f^{-1}\left(x\right)=y$
$\Rightarrow x=f\left(y\right)={\log }_{3}y$
$\Rightarrow y=3^x$
Therefore,
$y=f^{-1}\left(x\right)=3^x$