I need help to demonstrate the following or if you find a function I would appreciate it, I have already looked for many functions to see if any one fulfills it but none works for me and I can't think of how to prove it, I mean try to do it by defining uniform continuity and do not reach anything.
"Is there a growing function $ f: [0, \infty) \rightarrow {\mathbb {R}}$ such that neither she nor her inverse are uniformly continuous? If such a function exists, if not, demonstrate because it is not possible. "
First of all, Thanks.
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$\begingroup$Hint: consider something like:
$f(x) = x^2 + c1(n)$, for all 2n < x < 2n + 1
$f(x) = x^\frac{1}{2} + c2(n)$, for all 2n + 1 < x < 2n + 2
n - integers starting 0
c1(n) and c2(n) - some constant values
just think if you can find some function like that, define it for all integer x and make it growing (and even continuous), also think if this function can help you
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