By definition, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
In our equation, for each x value we have exactly one corresponding y-value, therefore, the following equation
[tex]y=\sqrt{x-3}[/tex]is indeed a function of x. The domain is the set of all possible inputs. The argument of a square root can't be negative, therefore, we have the following restriction:
[tex]x-3\geq0\implies x\geq3[/tex]In interval notation, our domain is:
[tex]\lbrack3,\infty)[/tex]