## Precalculus (6th Edition) Blitzer

The value of $f\left( -x \right)-f\left( x \right)$ is $6x$.
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 $6x$.