Find the inverse of y= e^x /(1+2e^x) could you guys tell me how you worked it out? i literally can't figure it out. .

Okay, here we go - tough with the limitations of this screen, but we'll go for it!

Like finding all inverse functions, first exchange x and y in the problem. Then, re-solve the problem to isolate y again. Then, replace y with F^-1(x). 
y=e^x/(1+2e^x) [starting equation]
x=e^y/(1+2e^y) [swap x and y]
x(1+2e^y)=e^y  [multiply both sides by (1+2e^y)
x+2xe^y=e^y    [distribute x]
x=e^y-2xe^y    [subtract 2xe^y from both sides]

x= e^y(1-2x)   [factor out e^y]
x/(1-2x) = e^y [divide both sides by (1-2x)]
ln(x/(1-2x)) = ln e^y  [take ln of both sides]

ln (x/(1-2x)) = y  [ln and e are inverses]

f^-1(x)= ln (x/(1-2x))

Go to desmos.com or use your TI graphing calculator to graph both the function and it's inverse to visually check that they are symetrical across the line y=x. You're all set.

The difference with this problem from others is the desire to quickly take the ln of all e terms. You need to wait until you have the variables in the right position before doing that.

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