Pre-Calculus - Evaluating the composition of functions and then determining the domain

f(x) = x/(x - 1); g(x) = sqrt(x - 3); Find the domain of (f o g)(x)

[SanguinariusUmbra]

The domain is wrong. If you just put *(3, infinity)* the square root of x-3 will turn 1 at some point and 1-1 would indeterminate the function. The domain of √x-3 is indeed [3, infinity) but the domain of (√x-3)-1 is [3, 4) ∪ (4, infinity), OR [3, infinity) - {4}. It can be 3 as well so I'm putting a closed domain.