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If I have a range between 0-1 , what functions can I use to increase the range other than log ? Using log will give a mapping between 0 to -7 ( around) , any other functions can I use regardless of the sign ?


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closed as not a real question by Thomas, Lord_Farin, Amzoti, Dennis Gulko, O.L. Jun 25 '13 at 14:31

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

Can you make your question more explicit? I'm not sure of what you are wanting to do, nor what qualifies as a "good" mapping? –  Clayton Jan 8 '13 at 20:09
@Clayton: Believe me, I read the question more that 10 times and can't find out what is the OP looking for. –  B. S. Jan 8 '13 at 20:11
Sorry, I updated it –  tnaser Jan 8 '13 at 20:41
I'm guessing, but are you asking for examples of maps $f:(0,1)\to \mathbb{R}$ with large image? –  user108903 Jan 8 '13 at 20:59
The cotangent of $\pi x$ maps your interval onto the entire number line. Can't do better than that. –  user53153 Jan 9 '13 at 7:11

1 Answer 1

Besides the logarithm, other functions which map $(0,1)$ onto an infinite interval include

  • $\dfrac{1}{x} + \dfrac{1}{x-1}$ (easy to evaluate)
  • $\cot \pi x$ (gets bonus points for being the kernel of the circular Hilbert transform)
  • $\dfrac{1}{x}\sin \dfrac{1}{x}$ (in case you find monotone functions too boring)
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