Let f : - 2 , 2 → ℝ be defined by f x = x x , - 2 < x < 0 x - 1 x , 0 ≤ x < 2 where x denotes the greatest integer function. If m and n respectively are the number of points in – 2 , 2 at which y = f x is not continuous and not differentiable, then m + n is equal to ________.

Step-by-step solution

Given, f : - 2 ,   2 → ℝ be defined by f x = x x , - 2 < x < 0 x - 1 x , 0 ≤ x < 2 ⇒ f x = - 2 x ,   - 2 < x < - 1 - x ,   - 1 ≤ x < 0 0 ,   0 < x < 1 x - 1 ,   1 ≤ x < 2 Now plotting the diagram of the above function we get, Now from above diagram we can say that, y = f x is same as y = f x Hence, the function is not continuous at one point and non differentiable at three points, so m = 1 ,   n = 3 Hence, m + n =