# Chapter 10 - Exponents and Radicals - 10.1 Radical Expressions and Functions - 10.1 Exercise Set - Page 635: 100

$\left[ -\dfrac{4}{3}, \infty \right)$

#### 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 $\left[ -\dfrac{4}{3}, \infty \right) .$

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