Example

What is the domain of the function $h(x)=\sqrt{x-5}$?

Solution

This function $h$ is defined for all real numbers except for those that make the radicand negative. Therefore, the domain must exclude all $x$-values for which $x-5<0$.

$x-5<0$ whenever $x<5$. So the domain includes only those real numbers for which $x\ge 5$.

The domain of $h$ is the set of all real numbers greater than or equal to $5$. That is,