Question

let $f(x)=2x^2 + x - 11$ and $g(x)=x - 1$. perform the function operation and then find the domain. $(f + g)(x)$ $(f + g)(x)=square$ (simplify your answer.)

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 substitute the given functions \(f(x) = 2x^{2}+x - 11\) and \(g(x)=x - 1\) into this formula.
\[
(f + g)(x)=f(x)+g(x)=(2x^{2}+x - 11)+(x - 1)
\]

Step2: Combine like terms

First, remove the parentheses: \(2x^{2}+x - 11+x - 1\). Then combine the \(x\) terms (\(x+x = 2x\)) and the constant terms (\(-11-1=-12\)).
\[
2x^{2}+(x + x)+(-11-1)=2x^{2}+2x-12
\]

Answer:

\(2x^{2}+2x - 12\)