Finding the inverse of functions involving e^x

[Math_Junkie]

1. y = 3 + x + e^x
2. y = e^x/(1+2e^x)

My attempts for both led me astray and I could not isolate the x. Any help?

Thanks in advance.

 

[mmm4444bot]

I'm not sure about (1). Are you familiar with the LambertW function?

For (2), I think the following steps will work.

Switch variables y <--> x

Now, solve for y:

Multiply both sides by the denominator

Expand the lefthand side

Subtract 2x e^y from both sides

Factor out e^y on the righthand side

Divide both sides by the other factor, in order to isolate the power of e

Switch to logarithmic form