I'm having a little trouble trying to prove a question on uniform continuity that is in one of my textbooks (which doesn't have answers, unfortunately).
The question asks:
"Is the function f(x) = x3+x uniformly continuous on R? Prove your answer"
I am almost certain that the answer is no for the simple reason that as x gets increasingly large the gaps get bigger so the same epsilon value won't work, but I'm not sure as to how to go about writing this in mathematical terms.
I know that for a function to be uniformly continuous |f(x) - f(x')|<epsilon whenever |x - x'|<delta for ALL x, x' that are elements of the subset, S, which in this case is R.
I would appreciate any help although preferably a proof that I can follow so that I can make the link to what I know to how to write it, if that makes sense.
Thanks in advance,