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

1 Answer
Rachel
Apr 9, 2017

[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)

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