- #1
nugget
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Homework Statement
Consider the function g : [0,∞) → R defined by g(x) = x + e−2x.
Given |g(x2) − g(x1)| < |x2 − x1| for all x1, x2 ∈ [0,∞) with x1 ≠ x2.
Is g a contraction on [0,∞)? Why?
Homework 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(x2) − g(x1)|<|x2 − x1|
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