Answer
\[{{f}^{-1}}\left( g\left( 1 \right) \right)=-1\]
Work Step by Step
The value of the given composite function can be obtained using the definition of composite functions and the values of $f$ and $g$ at the required points, which can be obtained very easily from the above table.
$\begin{align}
& {{f}^{-1}}\left( g\left( 1 \right) \right)={{f}^{-1}}\left( 1 \right) \\
& =-1
\end{align}$
Here, ${{f}^{-1}}\left( 1 \right)=-1$ because $f\left( -1 \right)=1$.
