Answer
a) $f(4)=16$
b) $f^{-1}(16)=4$
Work Step by Step
Substituting $x=
4
$ in the given function, $
f(x)=2^x
,$ results to
\begin{align*}\require{cancel}
f(4)&=2^4
\\&=
16
.\end{align*}
Hence, $
f(4)=16
$.
The point $(x,f(x))=
(4,16)
$ is a point on the given function. Since $f(x)$ is given to be one-to-one. Then by interchanging the $x$ and $y$ coordinates, the point $
(16,4)
$, is on the inverse $f^{-1}(x).$ Hence, $
f^{-1}(16)=4
$.
