Question 316300
First compute {{{f(-x)}}}: 


{{{f(x)=x^2-3x+7}}} Start with the given function.



{{{f(-x)=(-x)^2-3(-x)+7}}} Replace 'x' with -x



{{{f(-x)=x^2-3(-x)+7}}} Square -x to get {{{x^2}}}



{{{f(-x)=x^2+3x+7}}} Multiply -3 and -x to get 3x



Now let's evaluate {{{f(-x)-f(x)}}}



{{{f(-x)-f(x)}}} Start with the given expression.



{{{(x^2+3x+7)-(x^2-3x+7)}}} Plug in {{{f(-x)=x^2+3x+7}}} and {{{f(x)=x^2-3x+7}}} 



{{{x^2+3x+7-x^2+3x-7}}} Distribute.



{{{6x}}} Combine like terms.



So {{{f(-x)-f(x)=6x}}} when {{{f(x)=x^2-3x+7}}}