#y=3+x+e^x# ....find the inverse of y?

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Answer 1 · 2018-04-15T14:50:26

#x = y-3 - W(e^(y-3))#

Calling

#z = y-3-x# we have

#z = e^(y-3-z) rArr z e^z = e^(y-3) rArr z = W(e^(y-3))#

and finally

#x = y-3 - W(e^(y-3))#

Here #W(cdot)# is the Lambert function