How do we find the inverse of the function #y=e^(2x)/(7+e^(2x))#?

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Answer 1 · 2016-09-22T16:16:26

Inverse function of #f(x)=y=e^(2x)/(7+e^(2x))# is #y=1/2ln((7x)/(1-x))#

Let #f(x)=y=e^(2x)/(7+e^(2x))#

i.e. #(7+e^(2x))/e^(2x)=1/y# or

#7/e^(2x)+1=1/y# or

#7/e^(2x)=1/y-1=(1-y)/y# or

#e^(2x)=(7y)/(1-y)# or

#ln((7y)/(1-y))=2x# and hence

#x=1/2ln((7y)/(1-y))#

Hence inverse function of #f(x)=y=e^(2x)/(7+e^(2x))# is #y=1/2ln((7x)/(1-x))#