Answer
$(-\infty,5]$
Work Step by Step
$\bf{\text{Solution Outline:}}$
The domain of the given function, $
g(x)=\sqrt[4]{10-2x}
,$ 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}
10-2x\ge0
\\\\
-2x\ge-10
.\end{array}
Dividing both sides by a negative number (and consequently reversing the inequality symbol) the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-2x\ge-10
\\\\
x\le\dfrac{-10}{-2}
\\\\
x\le5
.\end{array}
Hence, the domain is the interval $
(-\infty,5]
.$
