Question

What is the domain and range of `y = ln((2x-1)/(x+1))`?

Answer 1

Domain is set of all positive real numbers greater than `1/2`
Range is the entire real number system.

Explanation:

Given log functions can take values that are either above 0 or below infinite, basically the positive side of the Real number axis.
So, `log(x)inRR " "AA x in RR^+`
Here, `x " is simply " (2x-1)/(x+1)`
So, `(2x-1)/(x+1)>0\impliesx!=0" "x>1/2`
Of course, the range of the log function is the entire real number system.

Note in the above answer, I did not regard the complex numbers at all.