To determine the domain of the function [tex]\( y = \sqrt{x} \)[/tex], we need to identify the values of [tex]\( x \)[/tex] for which the function is defined. A square root function is defined only when the expression inside the square root is non-negative because the square root of a negative number is not a real number.
The expression inside the square root in this case is [tex]\( x \)[/tex]. Therefore, the requirement for the function [tex]\( y = \sqrt{x} \)[/tex] to be defined is:
[tex]\[ x \geq 0. \][/tex]
This means that [tex]\( x \)[/tex] can be any non-negative number, including zero.
Expressing this in interval notation, the domain of [tex]\( y = \sqrt{x} \)[/tex] is:
[tex]\[ 0 \leq x < \infty. \][/tex]
Among the given options, this domain corresponds to:
[tex]\[ 0 \leq x < \infty. \][/tex]
So, the correct answer is:
[tex]\[ 0 \leq x < \infty. \][/tex]
