Domain range and inverse of natural log function

Let f be the function given by f(x)=ln(x/x-1)

A) what is the domain and range of f

B) what is the inverse of f

C) what is the range of the inverse,justify

So when I started this problem I got the domain to be (-infinity,0),(1,infinity) because the restriction in the domain of 1 and 0. For the range I think it is a limit issue but I don't know how to get that and for the inverse I can't figure out how to get rid of the y-1 in the denominator after I raise both sides under base e to get rid of the ln. Thanks!

Re: Domain range and inverse of natural log function

(a) agree with your domain.

for the range, consider the first domain interval ... as , and as , ... the range of the log function over this interval is .

now consider the other interval of the domain ... as , and as , ... the range of the log function over this interval is .

I'd say the range is all reals except y = 0

(b) inverse ...

(c) ... wouldn't the range of the inverse be the domain of the original function?