Question

what is (f + g)(x)?
f(x) = -5x
g(x) = x² + 6x + 5
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 \(f(x)= - 5x\) and \(g(x)=x^{2}+6x + 5\), we substitute these into the formula: \((f + g)(x)=-5x+(x^{2}+6x + 5)\)

Step2: Combine like terms

First, remove the parentheses: \(-5x+x^{2}+6x + 5\).
Then, combine the \(x\)-terms: \(-5x+6x=x\).
So the expression becomes \(x^{2}+x + 5\).

Answer:

\(x^{2}+x + 5\)