# What is the domain and range of  f(x) = 10/x?

Domain of $f \left(x\right) = \frac{10}{x}$ is $\left(- \infty , 0\right) \cup \left(0 , + \infty\right)$
Range of $f \left(x\right) = \frac{10}{x}$ is also $\left(- \infty , 0\right) \cup \left(0 , + \infty\right)$
$f \left(x\right)$ is defined for all Real values of $x$ except $x = 0$; so the Domain is all $\mathbb{R} - 0$ (which is another way of writing the union of open sets shown above).
Conversely, any Real value of $y$ except $y = 0$ can be solved for some value of $x$; so the Range is all $\mathbb{R} - 0$.