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

1 Answer
Rohan A.K
Jan 20, 2016

Domain is set of all positive real numbers greater than 1/212
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.

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