Problem on function definition I'm trying to solve this problem about functions: "Explain why $x^2-4=0$ is not a real function of real variable."
I have yet solved many similar problems, but now i have a doubt; is my solution correct ?
I give this solution to the problem:
1 - First of all, i search all the values of $x$ that satisfies $x^2-4 = 0$, obtaining obviously $x=-2\vee x=2$. I make this step in order to make the epression $x^2-4=0$ true.
This step is a sort of domain calulation.
2 - For every value of $x$ obtained in step 1, i check if exists one and only one value of $y$ (function definition); obviously the absence of the variable $y$ make it possible to assume any value.
3 - For one value of the domain $\lbrace-2,2\rbrace$ $y$ is not uniquely determined, so the relation $x^2-4=0$ is not a function.
Do you find this explanation correct ? 
Thank you for the answers.

Well we can say that the co-domain of this function is $\{0\}$ because $y=0$,we can say that domain is $\{-2,2\}$,since $\{-2,2\}$ is not an subset of $\mathbb{R}$ that contains an open set,thus $x^2-4=0$ is not a real function of real variable.
