Uniform Continuity of f(x) = 1/(|x|+1) on R: Epsilon-Delta Proof

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The discussion focuses on proving that the function f(x) = 1/(|x|+1) is uniformly continuous on R using an epsilon-delta approach. The key requirement is to establish a delta (d) for any given epsilon (e) such that if |x-y|<d, then |f(x)-f(y)|<e for all x, y in R. Participants express difficulty in finding an appropriate delta and inquire about potential algebraic techniques or tricks to simplify the proof. The conversation emphasizes the need for a clear method to demonstrate uniform continuity effectively. The thread highlights the importance of understanding the epsilon-delta definition in the context of this specific function.
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Homework Statement


Prove that f(x) = 1/(|x|+1) is uniformly continuous on R.

Homework Equations

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?
 
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