Question: is x uniformly continuous on r?
Answer: We know that for f to be continuous, then ∀ϵ>>0, ∃δ>0 such that if x0 and x ∈S and |x−x0| < ϵ, |f(x)−f(x0)| < δ must hold. ... Thus, f(x)=x is uniformly continuous on R.