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

Jan 20, 2016

Domain is set of all positive real numbers greater than $\frac{1}{2}$
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, $\log \left(x\right) \in \mathbb{R} \text{ } \forall x \in {\mathbb{R}}^{+}$
Here, $x \text{ is simply } \frac{2 x - 1}{x + 1}$
So, $\frac{2 x - 1}{x + 1} > 0 \setminus \implies x \ne 0 \text{ } x > \frac{1}{2}$
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.