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