#### Answer

\[{{g}^{-1}}\left( 7 \right)=2\]

#### Work Step by Step

This value of the given function can be obtained using the definition of functions and the value of $g$ at the required point.
Assume, ${{g}^{-1}}\left( 7 \right)=x$ , then $g\left( x \right)=7$.
Since the value of $g\left( x \right)=4x-1$ , thus we have
$\begin{align}
& 4x-1=7 \\
& 4x=8 \\
& x=2
\end{align}$
Thus, ${{g}^{-1}}\left( 7 \right)=x=2$.