in f(x)=ln(x/x-1) how would you write an exporession for f^-1(x), where f^-1(x) denotes the inverse of f(x)

Answer 1

I assume the correct expression is
y=f(x)=ln(x/(x-1))
taking inverse of ln(),
e^y = x/(x-1)
(x-1)e^y = x
x = e^y / (e(^y -1)
Therefore
f^-1(x) = e^x / (e(^x -1)

Answer 2

erratum:
f^-1(x) = e^x/(e^x-1)