Question

what is $(f + g)(x)$?
$f(x) = -2x^2 + 2x$
$g(x) = -4x$
write your answer as a polynomial or a rational function in simplest form.

Explanation:

Step1: Recall the definition of function addition

To find \((f + g)(x)\), we use the definition \((f + g)(x)=f(x)+g(x)\).
Given \(f(x)=-2x^{2}+2x\) and \(g(x) = - 4x\), we substitute these into the formula:
\((f + g)(x)=(-2x^{2}+2x)+(-4x)\)

Step2: Combine like terms

First, remove the parentheses: \(-2x^{2}+2x - 4x\).
Then, combine the \(x\)-terms: \(2x-4x=-2x\).
So, \((f + g)(x)=-2x^{2}-2x\)

Answer:

\(-2x^{2}-2x\)