Chapter 4 - Section 4.6 - Applications and Models of Exponential Growth and Decay - Summary Exercises on Functions: Domains and Defining Equations - Page 463: 8

$(-\infty, \infty)$

Since the index is odd in the given radical function, $ f(x)=\sqrt[3]{x^3+7x-4} ,$ then there are no restrictions in the value of the radicand. Hence, the domain is \begin{array}{l}\require{cancel} (-\infty, \infty) .\end{array}