Question

How do you find the domain of `f(x) = sqrt(x-9)`?

Answer 1

`[9, oo)`

Explanation:

The domain for a square root function is pretty simple. We cannot ever take the square root of a negative number. So, the value of `x` can never force the expression under the square root to be less than zero. So, let's find that value, and that will be our domain:

`0=x-9`
`9=x`

So, when `x=9`, the equation becomes `sqrt(9-9)` or `sqrt0`. So, our domain will be `9` to infinity, but will we include `9` or exclude it? Well, can we take the square root of zero? Yes, we can, so we can include `9`. We won't include `oo` however, because it is a limitless value.

The domain is `[9,oo)`