Final answer:
The domain of the function f(x) = (2x-3) / (|x-1|)+2 is all real numbers.
Step-by-step explanation:
In this function, there are two parts to consider: (2x-3) and |x-1|+2. Let's start with the second part, |x-1|+2. The absolute value function |x-1| gives the distance between x and 1 on the number line. Adding 2 to this gives the distance plus 2. So, this part of the function is always greater than or equal to 2.
Now, for the first part, (2x-3), there are no restrictions or limitations.
Therefore, the domain of the function f(x) = (2x-3) / (|x-1|)+2 is all real numbers.