Question

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

Answer 1

`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})`