Proving that a function is not a polynomial

Question: Prove that the function is not a polynomial.

My attempt (for which I got no marks as "it's not a proof") was to define a polynomial function as where is always equal to 1, and since does not equal to 1 for any given value of , then it's not a polynomial.

So how does one approach the question? I was thinking of rewriting as and then, since a polynomial function has a degree , and this function has a degree -1, it is by definition not a polynomial. But is that really a proof either? Not sure what to do.

Re: Proving that a function is not a polynomial

I think I would try assuming f(x) = P(x), where P(x) is a polynomial, and see if I could deduce a contradiction.

We would then have

Hmmm...