Two young mathematicians examine one (or two!) functions.

Check out this dialogue between two calculus students (based on a true story):
Devyn
Riley, I have a pressing question.
Riley
Tell me. Tell me everything.
Devyn
Think about the function
Riley
OK.
Devyn
Is this function equal to ?
Riley
Well if I plot them with my calculator, they look the same.
Devyn
I know!
Riley
And I suppose if I write
Devyn
Sure! But what about when ? In this case
Riley
Right, is undefined because we cannot divide by zero. Hmm. Now I see the problem. Yikes!
In the context above, are and the same function?
Suppose and are functions but the domain of is different from the domain of . Could it be that and are actually the same function?
Can the same function be represented by different formulas?
Let and . The domain of each of these functions is all real numbers. Which of the following statements are true?