Answer
$[-8, \infty)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
The domain of the given function, $
g(t)=\sqrt[4]{t+8}
,$ 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}
t+8\ge0
\\\\
t\ge-8
.\end{array}
Hence, the domain is the interval $
[-8, \infty)
.$