## Precalculus (6th Edition) Blitzer

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