The function is defined when the value inside the square root is positive, i.e. we must have $ x^2-5x+6>0 $. Factoring, we get $ (x-3)(x-2)>0 $. So either both factors in the left hand side are negative or they are both positive. They are both negative when $ x<2 $. They are both positive when $ x>3 $. So the domain of $ f(x) $ is $ x<2 \text{ or } x>3 $, or $ x \in \boxed{(-\infty, 2) \cup (3, \infty)} $ in interval notation.