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: Define sum of functions

$(f+g)(x) = f(x) + g(x)$

Step2: Substitute given functions

$(f+g)(x) = (2x^2 + x - 23) + (x - 1)$

Step3: Combine like terms

$(f+g)(x) = 2x^2 + (x + x) + (-23 - 1)$
$(f+g)(x) = 2x^2 + 2x - 24$

Step4: Find domain (polynomial domain)

Polynomial functions are defined for all real numbers.

Answer:

$(f+g)(x) = 2x^2 + 2x - 24$
Domain: All real numbers, or $(-\infty, \infty)$