Answer
$f(x) - g(x) + 10 = -x^2 + 5x + 13$
$\text{The domain is the set of all real numbers.}$
Work Step by Step
This exercise asks us to subtract $g(x)$ from $f(x)$ and then add $10$ to this sum. Let's write out the problem:
$f(x) - g(x) + 10 = (2x + 5) - (x^2 - 3x + 2) + 10$
Distribute terms first to get rid of the parentheses, paying attention to the signs:
$f(x) - g(x) + 10 = 2x + 5 - x^2 + 3x - 2 + 10$
Combine like terms:
$f(x) - g(x) + 10 = -x^2 + 5x + 13$
When we find the domain, we want to find which values of $x$ will cause the function to become undefined; in other words, we want to find any restrictions for $x$. In this exercise, $x$ can be any real number since there are no restrictions, so the domain is all real numbers.
