## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$\left[ -\dfrac{4}{3}, \infty \right)$
$\bf{\text{Solution Outline:}}$ 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 $\left[ -\dfrac{4}{3}, \infty \right) .$