Answer
The value of $g\left( f\left( -1 \right) \right)$ by the use of the function $f\left( x \right)={{x}^{2}}-x-4$ and $g\left( x \right)=2x-6$ is $-\underline{\mathsf{1}0}$.
Work Step by Step
Now, calculate $g\left( f\left( -1 \right) \right)$ by substituting x with $f\left( -1 \right)$: $x\to f\left( -1 \right)$
$\begin{align}
& g\left( f\left( -1 \right) \right)=2\left\{ f\left( -1 \right) \right\}-6 \\
& =2\left\{ {{\left( -1 \right)}^{2}}-\left( -1 \right)-4 \right\}-6 \\
& =2\left( 1+1-4 \right)-6 \\
& =2\left( -2 \right)-6
\end{align}$
$\begin{align}
& =-4-6 \\
& =-10 \\
\end{align}$
Therefore,
$g\left( f\left( -1 \right) \right)=-10$.
Hence, the value of $g\left( f\left( -1 \right) \right)$ by the use of the function $f\left( x \right)={{x}^{2}}-x-4$ and $g\left( x \right)=2x-6$ is $-\underline{\mathsf{1}0}$.
