Question

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

Answer 1

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(x)=1/x=1/0->` 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 `(-oo,0) uu (0,oo).`