Answer
The value of $\left( g-f \right)\left( x \right)$ with the functions $f\left( x \right)={{x}^{2}}-x-4$ and $g\left( x \right)=2x-6$ is $-{{x}^{2}}+3x-2$.
Work Step by Step
The function $\left( g-f \right)\left( x \right)$ can also be defined as $g\left( x \right)-f\left( x \right).$
Therefore,
$\begin{align}
& \left( g-f \right)\left( x \right)=\left( 2x-6 \right)-\left( {{x}^{2}}-x-4 \right) \\
& =2x-6-{{x}^{2}}+x+4 \\
& =-{{x}^{2}}+3x-2
\end{align}$
Hence,
$\left( g-f \right)\left( x \right)=-{{x}^{2}}+3x-2$.
Hence, the value of $\left( g-f \right)\left( x \right)$ with the functions $f\left( x \right)={{x}^{2}}-x-4$ and $g\left( x \right)=2x-6$ is $-{{x}^{2}}+3x-2$.
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