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

Apr 9, 2017

$\left[9 , \infty\right)$

#### 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 $\sqrt{0}$. 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 $\infty$ however, because it is a limitless value.

The domain is $\left[9 , \infty\right)$