Let [x] denotes the greatest integer less than or equal to x and f(x) = [ ^2 x] , then which of the following is true ?

Step-by-step solution

For x (- /4, /4) , we have -1 Squaring both sides, we get 0 ^2 x Therefore, f(x) = [ ^2 x] = 0 for all x (- /4, /4) . Since f(x) = 0 in a neighborhood of x = 0 , we have _ x 0 f(x) = 0 and f(0) = 0 . Thus, f(x) is continuous at x = 0 . Furthermore, since f(x) is constant in this neighborhood, f'(0) = 0 , meaning f(x) is differentiable at x = 0 . Answer: f(x) is continuous at x = 0