# How do I find the domain of y=1/x?

Oct 7, 2014

This is a rational function.

The denominator of a rational function cannot be $0$.

If the denominator is $0$ then the rational function is undefined .

If we can find the value(s) that would result in the denominator becoming $0$ then we could exclude those values when describing the domain of the function.

This is accomplished by setting the expression in the denominator equal to $0$.

$x = 0$ which would result in $f \left(x\right) = \frac{1}{x} = \frac{1}{0} \to$ Undefined

In this example the expression, $x$, will only be $0$ when $x$ is set to be $0$.

This means that the only value that the denominator , $x$, cannot assume is $0$.

The interval notation for the domain is $\left(- \infty , 0\right) \cup \left(0 , \infty\right) .$