Question

part 1 of 2
let $f(x)=x^2+x-2$ 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

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

Step3: Combine like terms

$(f+g)(x) = x^2 + (x+x) + (-2-1) = x^2 + 2x - 3$

Step4: Determine domain

The resulting function is a polynomial, so its domain is all real numbers, denoted as $(-\infty, \infty)$.

Answer:

$(f+g)(x) = x^2 + 2x - 3$
Domain: All real numbers, or $(-\infty, \infty)$