Question:

If $f: R^{+} \rightarrow R$ is defined as $f(x)=\log _{3} x$, then $r^{-1}(x)=$

Solution:

Given: f(x) = log3x

$f(x)=\log _{3} x$

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

$\Rightarrow x=3^{y}$

Thus, $f^{-1}(y)=3^{y}$.

Hence, $f^{-1}(x)=\underline{3}^{x}$.