Answer
a) $f(3)=8$
b) $f^{-1}(8)=3$
Work Step by Step
Substituting $x=3$ in the given function, $
f(x)=2^x
,$ results to
\begin{align*}\require{cancel}
f(3)&=2^3
\\&=
8
.\end{align*}
Hence, $
f(3)=8
$.
The point $(x,f(x))=(3,8)$ 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, $
(8,3)
$, is a point on the inverse $f^{-1}(x).$ Hence, $
f^{-1}(8)=3
$.
