To determine the domain of the function [tex]\( y = \sqrt{x} \)[/tex], we need to examine where the expression under the square root is defined in the real number system.
1. The function [tex]\( y = \sqrt{x} \)[/tex] involves taking the square root of [tex]\( x \)[/tex].
2. In the real number system, the square root is defined only for non-negative numbers because the square root of a negative number is not a real number.
Therefore, the restriction is that [tex]\( x \)[/tex] must be greater than or equal to 0. This can be expressed mathematically as:
[tex]\[ x \geq 0 \][/tex]
Putting this into interval notation, the domain of the function [tex]\( y = \sqrt{x} \)[/tex] is:
[tex]\[ 0 \leq x < \infty \][/tex]
So, the correct choice among the given options is:
[tex]\[ 0 \leq x < \infty \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{3} \][/tex]
