f(x) should give the chance of something happening, thats the reason for f(inf)=<1.(adsbygoogle = window.adsbygoogle || []).push({});

i used f(x)=1-exp(-a*x) until now, which is ok but f'(0) is not +inf. i would prefer a function with f(0)=+inf.

i want the function to be (monotonically) increasing at a decreasing rate (f' decreasing monotonically from +inf to 0)

does a function like this exist?

many thanks in advance!

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# Function with f(0)=0,f'(0)=+inf,f(inf)=<1

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