Question

let $f(x) = 5x + 3$ and $g(x) = x^2 - x + 2$. perform the function operation and then find the domain.
$f(x) + g(x)$

$f(x) + g(x) = \square$ (simplify your answer.)

Explanation:

Step1: Substitute function expressions

$f(x) + g(x) = (5x + 3) + (x^2 - x + 2)$

Step2: Combine like terms

$f(x) + g(x) = x^2 + (5x - x) + (3 + 2) = x^2 + 4x + 5$

Step3: Determine the domain

The resulting function is a polynomial, which is defined for all real numbers.

Answer:

$f(x)+g(x)=x^2 + 4x + 5$
Domain: All real numbers (or $(-\infty, \infty)$)