To determine the domain of the function [tex]\( y = \sqrt{x} \)[/tex], we need to identify the set of all possible values of [tex]\( x \)[/tex] for which the function is defined.
The square root function [tex]\( \sqrt{x} \)[/tex] is defined only when the expression under the square root is non-negative. This means that the argument of the square root, [tex]\( x \)[/tex], must be greater than or equal to zero.
Mathematically, this can be written as:
[tex]\[ x \geq 0 \][/tex]
This implies all values of [tex]\( x \)[/tex] that are greater than or equal to zero are within the domain of the function [tex]\( y = \sqrt{x} \)[/tex].
Thus, the domain of the function [tex]\( y = \sqrt{x} \)[/tex] is:
[tex]\[ 0 \leq x < \infty \][/tex]
Therefore, the correct option is:
[tex]\[ \boxed{0 \leq x < \infty} \][/tex]
