Question

what is the domain of the function $y = \sqrt3{x}$?
$\circ -\infty < x < \infty$
$\circ 0 < x < \infty$
$\circ 0 \leq x < \infty$
$\circ 1 \leq x < \infty$

Explanation:

Step1: Recall domain of cube root

The cube root function \( y = \sqrt[3]{x} \) is defined for all real numbers. Because for any real number \( x \) (positive, negative, or zero), we can take its cube root. For example, \( \sqrt[3]{-8} = -2 \), \( \sqrt[3]{8} = 2 \), and \( \sqrt[3]{0} = 0 \).

Step2: Match with options

The interval representing all real numbers is \( -\infty < x < \infty \).

Answer:

\( -\infty < x < \infty \) (the first option, assuming the first option is \( -\infty < x < \infty \))