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 function (y = \sqrt[3]{x}), the cube - root of a real number (x) is defined for all real values of (x). Let (x) be a real number. If (x=a^{3}), where (a\in R), then (\sqrt[3]{x}=a). When (x) is positive, say (x = 8=2^{3}), (\sqrt[3]{8}=2); when (x = 0), (\sqrt[3]{0}=0); when (x=-8=(- 2)^{3}), (\sqrt[3]{-8}=-2).

Answer:

(-\infty<x<\infty)