Answer
$(f - g)(x) = \frac{1}{x} +x- 2$
$\text{Domain: all real numbers except } 0$.
Work Step by Step
This exercise asks us to subtract $g(x)$ from $f(x)$. Let's write out the problem:
$(g - f)(x) = g(x) - f(x) = (\frac{1}{x}) - (2 - x)$
Distribute terms first to get rid of the parentheses, paying attention to the signs:
$(f - g)(x) = \frac{1}{x} +x-2$
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 $x$ so that we can exclude it from the domain.
In this exercise, $x$ can be any real number except $0$ since $0$ will make $\frac{1}{x}$ undefined.
