1. The problem asks for the domain of the function defined by the absolute value expression $|x^3 - 7|$. 2. The domain of a function is the set of all input values $x$ for which the function is defined. 3. Since $x^3 - 7$ is a polynomial, it is defined for all real numbers. 4. The absolute value function $|y|$ is also defined for all real numbers $y$. 5. Therefore, the composition $|x^3 - 7|$ is defined for all real numbers $x$. 6. Hence, the domain of $|x^3 - 7|$ is all real numbers, which can be written as $(-\infty, \infty)$. Final answer: The domain of $|x^3 - 7|$ is $\boxed{(-\infty, \infty)}$.