Question

Find the inverse of f(x)=\[\frac{ 1 }{ 1-x }\]

Answer 1

y=1/(1-x)
solve for x:
(1-x)y=1
1-x=1/y
-x=(1/y)-1
x=1-(1/y)

Answer 2

Now just replace x by f(x) and y by x, and voila, you're done.