Question

what is $(f - g)(x)$?
$f(x) = -3x^2 + 7x$
$g(x) = -x + 2$
write your answer as a polynomial or a rational function in simplest form.

Explanation:

Step1: Recall the definition of \((f - g)(x)\)

By the definition of function subtraction, \((f - g)(x)=f(x)-g(x)\).

Step2: Substitute the given functions

We know that \(f(x)=- 3x^{2}+7x\) and \(g(x)=-x + 2\). So we substitute these into the formula:
\((f - g)(x)=(-3x^{2}+7x)-(-x + 2)\)

Step3: Distribute the negative sign

When we distribute the negative sign to \(-x + 2\), we get:
\((f - g)(x)=-3x^{2}+7x+x - 2\)

Step4: Combine like terms

Combine the \(x\)-terms: \(7x+x = 8x\). So the simplified form is:
\((f - g)(x)=-3x^{2}+8x - 2\)

Answer:

\(-3x^{2}+8x - 2\)