Answer
The value of\[g\left( -1 \right)=-8\ \ \text{and}\ f\left( g\left( -1 \right) \right)=76\].
Work Step by Step
Put\[x=-1\ \ \text{in}\ \ g\left( x \right)=3x-5\ \ \text{to}\ \ \text{get}\ \ \text{the}\ \ \text{value}\ \ \text{of}\ \ g\left( -1 \right)\ \ \text{as}\ \ \text{follows:}\]
\[\begin{align}
& g\left( -1 \right)=3\left( -1 \right)-5 \\
& =-3-5 \\
& =-8
\end{align}\]
Now, put \[g\left( -1 \right)=-8\ \ \text{in}\ f\left( x \right)={{x}^{2}}-x+4\ \ \text{to}\ \text{get}\ \text{the}\ \text{value}\ \text{of}\ f\left( g\left( -1 \right) \right)\ \text{as}\ \text{follows:}\]
\[\begin{align}
& f\left( g\left( -1 \right) \right)={{\left( -8 \right)}^{2}}-\left( -8 \right)+4 \\
& =64+8+4 \\
& =76
\end{align}\]
The value of\[g\left( -1 \right)=-8\ \ \text{and}\ f\left( g\left( -1 \right) \right)=76\].
