1. The problem statement, all variables and given/known data Prove that f(x) = 1/(|x|+1) is uniformly continuous on R. 2. Relevant equations 3. The attempt at a solution This needs to be an e-d proof (epsilon-delta). So I suppose we should start with let e>0, then we want to find a d such that for all x,y in R, if |x-y|<d then |f(x)-f(y)|<e. I'm having trouble locating a d that will work, is there some algebra trick or other type of trick that can help me?