Answer
$(f + g)(x) = 2 - x + \frac{1}{x}$
$\text{Domain: all real numbers except }0$
Work Step by Step
This exercise asks us to add $g(x)$ to $f(x)$. Let's write out the problem:
$(f + g)(x) = f(x) + g(x) = (2 - x) + (\frac{1}{x})$
Distribute terms first to get rid of the parentheses, paying attention to the signs:
$(f + g)(x) = f(x) + g(x) = 2 - x + \frac{1}{x}$
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 for $0$ since $0$ will make $\frac{1}{x}$ undefined.
