# What is the domain and range of the function f(x) =sqrt(x-9)?

Oct 14, 2017

Domain: $\left(- \infty , 9\right) \cup \left(9 , \infty\right)$
Range: $\left(0 , \infty\right)$

#### Explanation:

Domain:
Domain = x-values

When we find the domain of a root, we first have to set it to $\cancel{\ge} 0$, as a root of something can't be a negative number. So the restriction for the domain looks like this:
$\sqrt{x - 9} \cancel{\ge} 0$ simplify:
$x - 9 \cancel{\ge} 0$
$x \cancel{\ge} 9$ So if you write the domain in interval notation, it looks like this:
$\left(- \infty , 9\right) \cup \left(9 , \infty\right)$

Range:
Range = y-values
The range of a square root function is $> 0$
So if you write the range in interval notation, it looks like this:
$\left(0 , \infty\right)$