Let f x = sin x - x x - x , x ∈ - 2 , - 1 max 2 x , 3 x , x < 1 1 , otherwise where t denotes greatest integer ≤ t . If m is the number of points where f is not continuous and n is the number of points where f is not differentiable, the ordered pair m , n is:

Step-by-step solution

Given, f x = sin x - x x - x , x ∈ - 2 , - 1 max 2 x , 3 x , x < 1 1 , otherwise On simplifying we get, f x = sin x + 2 x + 2 , x ∈ - 2 , - 1 max 2 x , 0 ,    x ∈ - 1 , 1 1 otherwise f - 2 + = lim h → 0 f - 2 + h = lim h → 0 sin - 2 + h + 2 - 2 + h + 2 = lim h → 0 sinh h = 1 f is continuous at x = - 2 f - 1 - = lim h → 0 sin - 1 - h + 2 - 1 - h + 2 = sin 1 f - 1 = f - 1 * = 0 f 1 + = 1   &   f 1 - = 0 ⇒ f is not continuous at x = 1 f is con