This time I'd like to ask for your opinion on a "mathematical" proof I wrote as an answer to a problem from my teacher:
Problem: Be f(x) continuous for every x, passes through the point (1,2) (f(1) = 2), it is known that for every x there is
prove that f(x) > x for every x.
It is given that f(1)=2 which means that f(x)> x at least at some point.
According to the intermediate value theorem, for f(x) < x to exist
f(x) = x has to exist at least once in the interval (-oo,oo).
BUT it is given that f(x) x for every x.
Therefore f(x) > x , always.
Would that work as a "mathematical" proof for college etc..?