# What is the domain of h(x)=sqrt(x-2)?

Jun 17, 2018

$x \in \left[2 , \infty\right)$

#### Explanation:

For radical functions, we cannot have a quantity less than $0$ inside the square root.

In this case, we know that $h \left(2\right) = 0$, but if $x$ is decreased any more than this, the radical will be undefined.

So we know that $x = 2$ is the minimum value of the domain. As we increase $x$, we have no issues as the radical always contains a positive number. So $x \to \infty$.

So the domain would be all values of $x \ge 2$, or

$x \in \left[2 , \infty\right)$