If [x]^2-5[x]+6=0 , where [ ] denotes the greatest integer function, then

Step-by-step solution

Given [x]^2 - 5[x] + 6 = 0 , let y = [x] to obtain y^2 - 5y + 6 = 0 . Factoring yields (y-2)(y-3) = 0 , so y = 2 or y = 3 . Since y = [x] , the solution splits into two cases: either [x] = 2 or [x] = 3 . By definition of the greatest integer function, [x] = 2 implies 2 x The union of these intervals is 2 x Final answer: C