Answer
\[f\left( g\left[ h\left( 1 \right) \right] \right)=25\]
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
$\begin{align}
& f\left( g\left[ h\left( 1 \right) \right] \right)=f\left( g\left[ 4 \right] \right) \\
& =f\left( 4\times 4-1 \right) \\
& =f\left( 15 \right)
\end{align}$
Now simplify further to get,
$\begin{align}
& f\left( 15 \right)=2\left( 15 \right)-5 \\
& =25
\end{align}$
