Question

what is $(f + g)(x)$?
$f(x) = -x^2 - 6x$
$g(x) = x^2 + 7x$
write your answer as a polynomial or a rational function in simplest form.

Explanation:

Step1: Recall the definition of function addition

The sum of two functions \((f + g)(x)\) is defined as \(f(x) + g(x)\). So we need to add the expressions for \(f(x)\) and \(g(x)\) together.
Given \(f(x)=-x^{2}-6x\) and \(g(x)=x^{2}+7x\), then \((f + g)(x)=(-x^{2}-6x)+(x^{2}+7x)\).

Step2: Combine like terms

First, combine the \(x^{2}\) terms: \(-x^{2}+x^{2}=0\).
Then, combine the \(x\) terms: \(-6x + 7x=x\).

Answer:

\(x\)