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