For this case we have that, by definition, the domain of a function is given by all the values for which the function is defined.
Having said that, we have the following function:
![r (x) = \frac {2x} {x-1}](https://img.qammunity.org/2020/formulas/mathematics/middle-school/qpna8u83pn356osmpec1mebjsdkynriaxj.png)
It is not defined when the denominator is equal to 0. That is:
![x-1 = 0\\x = 0 + 1\\x = 1](https://img.qammunity.org/2020/formulas/mathematics/middle-school/r38kb5ksrpnqgytfdmammnlox0k7v9m72q.png)
Thus, the domain of r (x) is given by all real numbers except 1.
Answer:
all real numbers except 1.
Option A