Case 1: if then .
Case 2: if then .
So your friend was essentially telling you the same thing I just did!.
and so .
A friend of mine pointed out that I could show this in the following manner:
If then there exist x in such that f(x)= E. Since , then so and so . Therefore ..
I do not know how to continue. If , what then? Should I be doing all of this differently?