- #1
annaphys
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Homework Statement
##f:= tanh = \frac{e^x-e^{-x}}{e^x+e^{-x}}##
Prove that
##f^{-1}(x)= \sum\limits_{k=0}^{\infty} \frac{x^{2k+1}}{2k+1}## for all x in (-1,1)
The Attempt at a Solution
I also found the inverse function to be:
##f^{-1}(x)= \frac{1}{2}ln(\frac{1+x}{1-x})##
I tried working with the taylor polynomial but unfortunately nothing came out of it. Could someone point me in the right direction?
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