How do you find the inverse of #y = e^x/(1 + 4 e^x)#?

1 Answer
May 15, 2018

#x =\ln(\frac{y}{1-4y})#

Explanation:

This question would be a "solving for the inverse of a rational functions question" and you would follow the same standard
procedure as you would for solving those equations.

First multiply both sides by #1+4e^x# :
#y(1+4e^x) =e^x#
#y+4e^xy - e^x = 0#
#4e^xy - e^x = -y# , factor #e^x#
#e^x(4y - 1) = -y#
#e^x= \frac{-y}{4y - 1} = \frac{y}{1-4y} #
#x = \ln(\frac{y}{1-4y})#