Question

What is the domain of `sqrt(x^2-9)`?

Answer 1

The domain of this expression is `{x|x < -3` or `x > 3}`.

Explanation:

To find restrictions to the domain of a square root expression, you must determine which values of the variable will make the radicand have a negative value.

`x^2 - 9 < 0`
`x^2 - 9 + 9 < 0 + 9`
`x^2 < 9`
`sqrtx^2 < sqrt9`
`x < +-3`

This actually tells us that `x` cannot be between `-3` and `3`, inclusive. Therefore `x` must be less than `-3` or greater than `3`.