Answer
$\left( -\infty,10 \right]$
Work Step by Step
$\bf{\text{Solution Outline:}}$
The domain of the given function, $
g(x)=\sqrt[4]{10-x}
,$ 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}
10-x\ge0
\\\\
-x\ge-10
\\\\
x\le\dfrac{-10}{-1}
\\\\
x\le10
.\end{array}
Hence, the domain is the interval $
\left( -\infty,10 \right]
.$
