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Homework Help: Natural Log and Inverse derivatives

  1. Nov 29, 2007 #1
    1. The problem statement, all variables and given/known data
    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.

    3. 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. Im not sure how to do this one, help is appreciated =]
  2. jcsd
  3. Nov 29, 2007 #2


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    Homework Helper

    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
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