Question

How do you find the domain of `y=(2x)/(x+9)`?

Answer 1

`x!=-9` or interval notation `(-oo,-9) U (-9,oo)`

Explanation:

If a value of `x` results in `y` being "undefined", that value of `x` is not included in the domain. The domain is the allowed values of `x`.

For a rational equation like this example, dividing by zero will result in an undefined `y`. So, the denominator should not equal zero.

`x+9!=color(white)a0`
`color(white)(a)-9color(white)(aa)-9`

`x!=-9`

A value of `-9` will result in a zero in the denominator, so `-9` is not be included in the domain.

In interval notation, this is written as `(-oo,-9)U(-9,oo)`