#### Answer

$[6, \infty)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
The domain of the given function, $
f(x)=\sqrt{x-6}
,$ is the permissible values of $x.$
$\bf{\text{Solution Details:}}$
With an even index (index equals $
2
$), then the radicand should be a nonnegative number. Hence,
\begin{array}{l}\require{cancel}
x-6\ge0
\\\\
x\ge6
.\end{array}
Hence, the domain is the interval $
[6, \infty)
.$