Find the inverse Function?

Question

J(x)=2^x/(1+2^x)

Answer 1

switch variables and solve for y:

x = 2^y/(1+2^y)
x + x*2^y = 2^y
x = 2^y(1-x)
2^y = x/(1-x)
J^-1 = y = log₂ x/(1-x)