Answer
The value of $f\left( -x \right)-f\left( x \right)$ is $6x$.
Work Step by Step
By replacing x by –x in the given function, we get the expression for $f\left( -x \right)$ as follows
$\begin{align}
& f\left( -x \right)={{\left( -x \right)}^{2}}-3\left( -x \right)+7 \\
& ={{x}^{2}}+3x+7
\end{align}$
So, calculate the value of the expression $f\left( -x \right)-f\left( x \right)$ as follows
$\begin{align}
& f\left( -x \right)-f\left( x \right)={{x}^{2}}+3x+7-\left( {{x}^{2}}-3x+7 \right) \\
& ={{x}^{2}}+3x+7-{{x}^{2}}+3x-7 \\
& =6x
\end{align}$
Therefore, the given value of $f\left( -x \right)-f\left( x \right)$ is $6x$.
