>>43
Why aren't you canceling the x before substituting? If you can cancel out the singularity, you are certainly allowed to do so. In fact, it would be foolish not to. I honestly don't see the rationale behind this lack of simplification.
So then, following your reasoning x^2 is discontinuous at 0 also?
Also, if you want to be pedantic with definitions, functions aren't sets. The range of a function is a set, as is the domain. A function is simply a rule that assigns elements of one set(domain) to elements of another set(range).
If you don't even know this, I think you're in a bit over your head.