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?