Question

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

Explanation:

Step1: Recall the domain of cube root function

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

Step2: Match with the options

The set of all real numbers is represented as \( -\infty < x < \infty \). The other options restrict \( x \) to positive numbers (with or without zero) or numbers greater than or equal to 1, which is not correct for the cube root function.

Answer:

\( -\infty < x < \infty \)