Answer
The inverse function is,
${{f}^{-1}}\left( x \right)=\frac{1}{4}\left( {{x}^{2}}+7 \right)$
Work Step by Step
Consider the given function,
$y=\sqrt{4x-7}$
Square both sides to get,
$\begin{align}
& {{y}^{2}}=4x-7 \\
& x=\frac{1}{4}\left( {{y}^{2}}+7 \right)
\end{align}$
Therefore,
${{f}^{-1}}\left( x \right)=\frac{1}{4}\left( {{x}^{2}}+7 \right)$
