Answer
$\left[ -\dfrac{4}{3}, \infty \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
The domain of the given function, $
f(t)=\sqrt[6]{4+3t}
,$ 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}
4+3t\ge0
\\\\
3t\ge-4
\\\\
t\ge-\dfrac{4}{3}
.\end{array}
Hence, the domain is the interval $
\left[ -\dfrac{4}{3}, \infty \right)
.$
