Answer
$\left[ -\dfrac{2}{5}, \infty \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
The domain of the given function, $
h(z)=-\sqrt[6]{5z+2}
,$ is the permissible values of $x.$
$\bf{\text{Solution Details:}}$
With an even index (index equals $
6
$), then the radicand should be a nonnegative number. Hence,
\begin{array}{l}\require{cancel}
5z+2\ge0
\\\\
5z\ge-2
\\\\
z\ge-\dfrac{2}{5}
.\end{array}
Hence, the domain is the interval $
\left[ -\dfrac{2}{5}, \infty \right)
.$
