What is the domain of the function [tex]$y=\sqrt{x}$[/tex]?

A. [tex]-\infty\ \textless \ x\ \textless \ \infty[/tex]
B. [tex]0\ \textless \ x\ \textless \ \infty[/tex]
C. [tex]0 \leq x\ \textless \ \infty[/tex]
D. [tex]1 \leq x\ \textless \ \infty[/tex]



Answer :

To determine the domain of the function [tex]\( y = \sqrt{x} \)[/tex], we need to identify all the possible values of [tex]\( x \)[/tex] for which the function is defined. The domain of a function is the set of all permissible input values (i.e., values of [tex]\( x \)[/tex]).

1. The function [tex]\( \sqrt{x} \)[/tex] involves a square root.
2. For real numbers, the square root function [tex]\( \sqrt{x} \)[/tex] is only defined when [tex]\( x \)[/tex] is non-negative because the square root of a negative number is not a real number.
3. This implies that [tex]\( x \)[/tex] must be greater than or equal to 0.

Given these points, we conclude:
- [tex]\( x \)[/tex] cannot be negative because the square root of a negative number is not defined in the set of real numbers.
- [tex]\( x \)[/tex] can be zero or any positive number.

Thus, the domain of [tex]\( y = \sqrt{x} \)[/tex] is all [tex]\( x \)[/tex] such that [tex]\( x \)[/tex] is greater than or equal to 0.

In mathematical notation, this is expressed as [tex]\( 0 \leq x < \infty \)[/tex].

Therefore, the correct choice among the options provided is:

[tex]\[ \boxed{0 \leq x < \infty} \][/tex]

This corresponds to option 3.