Question: Let $f: R \rightarrow R^{+}$be defined by $f(x)=a^{x}, a>0$ and $a \neq 1$. Write $f^{-1}(x)$.
Solution:
Let $f^{-1}(x)=y$ $\ldots(1)$
$\Rightarrow f(y)=x$
$\Rightarrow a^{y}=x$
$\Rightarrow y=\log _{a} x$
$\Rightarrow f^{-1}(x)=\log _{a} x$ $[$ from (1)]
