Question

inverse f(x) = ln(x/x-1)

Answer 1

Maybe this will help
The inverse of the natural log is \[e^{x}\]

Answer 2

y=ln(x/x-1),
e^y=x/x-1
(e^y)x- e^y=x
x= e^y/(e^y-1).
now plug x at the place of y.
inverce of F(x)= (e^x)/(e^x-1)