How to find the inverse of this function

f(x) = e^x/(1+2e^x)

not sure how to even start this one- e^x is in both top and bottom, i know you need to use log but not sure how. any help is much appreciated, thanks.

f(x) = e^x/(1+2e^x) = y
y(1+2e^x) = e^x =>y + 2ye^x = e^x
=>y= (1-2y)e^x
=>y/(1-2y) = e^x
take log to the base e (ln) both side
ln(y/(1-2y)) = x
=>inverse of f(x) = ln(x/(1-2x))

Switch x and y,
x = e^y/(1+2e^y)
=> x+2xe^y = e^y
=> e^y = x/(1-2x)
=> f^-1(x) = y = ln[x/(1-2x)]

hint ; you have y = 1 / [ e^(-x) + 2 ]...solve for e^(-x) , then x = inverse function , g(y)