Question

let $f(x) = 2x^2 + x - 23$ 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 \(f(x)+g(x)\).
Given \(f(x)=2x^{2}+x - 23\) and \(g(x)=x - 1\), we substitute these into the formula:
\((f + g)(x)=f(x)+g(x)=(2x^{2}+x - 23)+(x - 1)\)

Step2: Combine like terms

First, combine the \(x\) terms: \(x+x = 2x\)
Then, combine the constant terms: \(-23-1=-24\)
The \(2x^{2}\) term remains as it is. So we have:
\((f + g)(x)=2x^{2}+2x - 24\)

Answer:

\(2x^{2}+2x - 24\)