Question

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

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

Answer 1

Answer: (B)

$3^x$

Given, $f\left(x\right)={\log }_{3}x$

Let $y={\log }_{3}x$

$\Rightarrow 3^y=x$

Replacing $x$ and $y$

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

Hence, option B is correct.