Natural Log and Inverse derivatives

[chris40256]

Homework Statement

Let f be the function given by f(x) = ln [ x/ (x-1)]
(a) What is the domain of f?
(b) What is the value of the derivative of f at x = -1.
(c) Write an expression for f^(-1) of x, where f^(-1) denotes the inverse function of f.

The Attempt at a Solution

a. x / x-1 has to be greater then 0 and x cannot equal 1. So i put the domain as all reals except 0 and 1
b. I separated the equation to lnx - lnx-1 and then took the derivative which i found to be 1/x - 1/x-1 and then plugged -1 into that getting -1/2
c. I am not sure how to do this one, help is appreciated =]

 

[rock.freak667]

a) and b) Look correct to me

for part c) you ley y=ln [ x/ (x-1)] and then find x in terms of y
and f^(-1)(x) will be the expression you found when you replace y by x