Answer
$g(x) - f(x) = x^2 - 5x - 3$
$\text{The domain is the set of all real numbers.}$
Work Step by Step
This exercise asks us to subtract $f(x)$ from $g(x)$. Let's write out the problem:
$g(x) - f(x) = (x^2 - 3x + 2) - (2x + 5)$
Distribute terms first to get rid of the parentheses, paying attention to the signs:
$g(x) - f(x) = x^2 - 3x + 2 - 2x - 5$
Combine like terms:
$g(x) - f(x) = x^2 - 5x - 3$
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.
