chris40256
Nov29-07, 03:47 PM
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 =]
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 =]