Question

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

Explanation:

Step1: Recall cube root function domain

The cube root function \( y = \sqrt[3]{x} \) is defined for all real numbers. Because for any real number \( x \), whether positive, negative, or zero, we can take its cube root. For example, \( \sqrt[3]{-8} = -2 \), \( \sqrt[3]{0} = 0 \), \( \sqrt[3]{8} = 2 \). So there are no restrictions on \( x \) in the real number system.

Step2: Match with options

The option \( -\infty < x < \infty \) represents all real numbers, which is the domain of \( y=\sqrt[3]{x} \).

Answer:

\( -\infty < x < \infty \) (the option with \( -\infty < x < \infty \))