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

Explanation:

Step1: Recall the property of cube - root function

For the cube - root function (y = \sqrt[3]{x}), we know that for any real number (x), the cube - root (\sqrt[3]{x}) is defined. Let (x) be a real number. If (x) is positive, say (x = 8), then (\sqrt[3]{8}=2); if (x = 0), then (\sqrt[3]{0}=0); if (x) is negative, say (x=-8), then (\sqrt[3]{-8}=-2).

Step2: Determine the domain

The domain of a function is the set of all possible input values (values of (x)) for which the function is defined. Since for any real number (x) (i.e., (x\in(-\infty,\infty))), the function (y = \sqrt[3]{x}) is well - defined.

Answer:

(-\infty<x<\infty)