Answer
$\frac{f}{g}(x) = 2x - x^2$
$\text{Domain: all real numbers except } 0$.
Work Step by Step
This exercise asks us to divide one function by another. Let's write out the problem:
$\frac{f}{g}(x) =f(x) \div g(x) = \frac{2 - x}{\frac{1}{x}}$
When we divide by a fraction, we multiply by its reciprocal:
$\frac{f}{g}(x) =f(x) \div g(x) = (2 - x)(x)$
Multiply:
$\frac{f}{g}(x) =f(x) \div g(x) = 2x - x^2$
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 them from the domain.
In this exercise, $\frac{1}{x}$ is undefined when $x=0$, so the domain is any real number except for $0$.
