Given f(x)= ((2+In x)/(2-In x)) find f(x) inverse

Answer 1

Let y = (2 + lnx) / (2 - lnx)

Switch x and y: x = (2 + lny) / (2 - lny)

Solve for y; 2x - xlny = 2 + lny

lny + xlny = 2x - 2

lny(1 + x) = 2(x - 1)

lny = 2(x - 1) / (x + 1)

y = e^{2(x - 1)/(x + 1)} = f^-1(x)