#### Answer

\[g\left( f\left[ h\left( 1 \right) \right] \right)=11\]

#### Work Step by Step

The value of the given composite function can be obtained using the definition of composite functions and the values of $f$ , $g$ and $h$ at the required points.
Now, $h\left( 1 \right)={{1}^{2}}+1+2=4$ , thus we have
$\begin{align}
& g\left( f\left[ h\left( 1 \right) \right] \right)=g\left( f\left[ 4 \right] \right) \\
& =g\left( 2\times 4-5 \right) \\
& =g\left( 3 \right)
\end{align}$
Now simplify further to get,
$\begin{align}
& g\left( 3 \right)=4\left( 3 \right)-1 \\
& =11
\end{align}$