Answer
The values of the function at the given points are $g\left( -1 \right)=-8$ and $f\left( g\left( -1 \right) \right)=76$
Work Step by Step
Substitute the value of $x=-1$ in $g\left( x \right)$ to get $g\left( -1 \right)$ as follows:
$\begin{align}
& g\left( x \right)=3x-5 \\
& g\left( -1 \right)=3\cdot \left( -1 \right)-5 \\
& =-3-5 \\
& =-8
\end{align}$
Calculate the value of $f\left( g\left( -1 \right) \right)$ by putting the value $x=g\left( -1 \right)$ in the function $f\left( x \right)$ as follows:
$\begin{align}
& f\left( x \right)={{x}^{2}}-x+4 \\
& f\left( g\left( -1 \right) \right)={{\left( -8 \right)}^{2}}-\left( -8 \right)+4 \\
& =64+8+4 \\
& =76
\end{align}$
Therefore, the values of function $g\left( -1 \right)$ and $f\left( g\left( -1 \right) \right)$ are $-8$ and $76$ , respectively.
