Answer
$f(x) - 2g(x) = -2x^2 + 8x + 1$
$\text{The domain is the set of all real numbers.}$
Work Step by Step
This exercise asks us to subtract $2$ times $g(x)$ from $f(x)$. Let's write out the problem:
$f(x) - 2g(x) = (2x + 5) - 2(x^2 - 3x + 2)$
Distribute terms first to get rid of the parentheses, paying attention to the signs:
$f(x) - 2g(x) = 2x + 5 - 2x^2 + 6x - 4$
Combine like terms:
$f(x) - 2g(x) = -2x^2 + 8x + 1$
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.