(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the function g : [0,∞) → R defined by g(x) = x + e^{−2x}.

Given |g(x_{2}) − g(x_{1})| < |x_{2}− x_{1}| for all x_{1}, x_{2}∈ [0,∞) with x_{1}≠ x_{2}.

Is g a contraction on [0,∞)? Why?

2. Relevant equations

I think we are intended to use the given equation and the CMT

CMT states that |f(x)-f(y)|=c|x-y|, where x,y∈R.

Which is similar to |g(x_{2}) − g(x_{1})|<|x_{2}− x_{1}|

3. The attempt at a solution

I really don't know where to begin with this; I'm not simply after the answer though, just a prod in the right direction would be great

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# Homework Help: Contraction Mapping Theorem Question

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