Compute the domain of the function $$f(x)=\frac{1}{\lfloor x^2-7x+13\rfloor}.$$
+128460 This one is a little hard to think about....
The function x^2 - 7x + 13 will never = 0 since it lies wholly above the x axis
Since we cant divide by 0, we actually want to find the x values where
x^2 -7x + 13 = 1
The two x values that make this true will produce a floor value of 1
The two solutions that we find will be included in the domain....all real numbers between these WILL NOT be in the domain since they will make the floor value = 0 and we can't divide by that
So rearranging, we have
x^2 -7x + 12 = 0 factor
(x - 3) ( x - 4) = 0
Setting each factor to 0 and solving for x produces x =3 and x = 4
So....the domain will be (-inf. 3 ] U [4, inf )
This graph seems to confirm our answer : https://www.desmos.com/calculator/df9v0bh5wt
