Compute the domain of the function$$f(x)=\frac{1}{\lfloor x^2-7x+13\rfloor}.$$

The function is undefined when the floor function is 0, which happens when x2−7x+13=0. Factoring the quadratic, we get [x^2 - 7x + 13 = (x - 3)(x - 4) = 0.]Therefore, the domain is (-infty,3) U (3,4) U (4,infty).