#### Answer

$[9, \infty)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
The domain of the given function, $
f(x)=\sqrt[4]{x-9}
,$ is the permissible values of $x.$
$\bf{\text{Solution Details:}}$
With an even index (index equals $
4
$), then the radicand should be a nonnegative number. Hence,
\begin{array}{l}\require{cancel}
x-9\ge0
\\\\
x\ge9
.\end{array}
Hence, the domain is the interval $
[9, \infty)
.$