Question

what is $(f + g)(x)$?
$f(x) = x^2 + 6x$
$g(x) = x^2 - 4$
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 \(g(x)\).
Given \(f(x)=x^{2}+6x\) and \(g(x)=x^{2}-4\), then \((f + g)(x)=f(x)+g(x)=(x^{2}+6x)+(x^{2}-4)\).

Step2: Combine like terms

First, combine the \(x^{2}\) terms: \(x^{2}+x^{2}=2x^{2}\). The \(6x\) term remains as it is, and the constant term is \(- 4\). So putting it all together, we have \(2x^{2}+6x - 4\).

Answer:

\(2x^{2}+6x - 4\)