Answer
The value of $\left( gof \right)\left( x \right)$ by the use of the functions $f\left( x \right)={{x}^{2}}-x-4$ and $g\left( x \right)=2x-6$ is $2{{x}^{2}}-2x-14$.
Work Step by Step
We know that the function $\left( gof \right)\left( x \right)$ can also be defined as $g\left( f\left( x \right) \right).$
Therefore, $\left( gof \right)\left( x \right)=g\left( {{x}^{2}}-x-4 \right)$
Now, substitute the value of x with ${{x}^{2}}-x-4$; that is, $x\to {{x}^{2}}-x-4$ in $g\left( x \right).$
Thus,
$\begin{align}
& \left( gof \right)\left( x \right)=2\left( {{x}^{2}}-x-4 \right)-6 \\
& =2{{x}^{2}}-2x-8-6 \\
& =2{{x}^{2}}-2x-14
\end{align}$
Therefore,
$\left( gof \right)\left( x \right)=2{{x}^{2}}-2x-14$.
Hence, the value of $\left( gof \right)\left( x \right)$ by the use of the functions $f\left( x \right)={{x}^{2}}-x-4$ and $g\left( x \right)=2x-6$ is $2{{x}^{2}}-2x-14$.
