Question

which represents the domain of $y = x^{\frac{1}{3}} - 1$?
options: $-1,\infty)$ , $1,\infty)$ , $(-\infty, -1$ , $(-\infty, \infty)$

Explanation:

Step1: Rewrite the radical term

$x^{\frac{1}{3}} = \sqrt[3]{x}$

Step2: Analyze cube root domain

Cube roots accept all real numbers, since $\sqrt[3]{x}$ is defined for any real $x$.

Step3: Confirm full function domain

The $-1$ term does not restrict the domain, so all real numbers are allowed.

Answer:

D. $(-\infty, \infty)$