Is there a way to convert a function g(x) so that the result lies between [0,1]? Thank you in advance.
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2Multiply it by zero. – Hayden Mar 30 '14 at 23:05
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Or compose it with the absolute value of $\sin$, that is, use $x\mapsto |\sin(g(x))|$. – Git Gud Mar 30 '14 at 23:06
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If you function is $\ge 0$, use the function $$ x\to \frac x{1+|x|} $$
In general, use $$ x\to \frac 12 \left(1+ \frac x{1+|x|}\right) $$ You hence have a one to one transformation: link to the plot
Another one is of course $$ x\to \frac 1\pi \arctan x + \frac 12 $$
mookid
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Thank you very much for help! In fact I have a differential equation. I apply Ito and I get g(ft) and I need a way to make sure that this lies between [0,1]. Sorry, I have not much idea about the science and I m in trouble now! – emy Mar 30 '14 at 23:14
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I m sorry...what do you mean open a new question...sorry, I m new in this website and I m not very familiar with the rules. Sure your answer gives me an idea how to go on. Thank you. – emy Mar 30 '14 at 23:19
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I have edited with another answer. To understand the way the site works, take the tour. – mookid Mar 30 '14 at 23:21
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I mean that your problem with Ito formula looks like it is a whole different problem, and deserves more than a commentary ;) – mookid Mar 30 '14 at 23:22
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Thank you very much. I will make a new more detailed question to refer this as well. – emy Mar 30 '14 at 23:24