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

1 Answer
Apr 9, 2017

Answer:

#[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)#