Let f : R → R be a function defined as f x = 3 1 - | x | 2 if | x | ≤ 2 0 if | x | > 2 . Let g : R → R be given by g ( x ) = f ( x + 2 ) - f ( x - 2 ) . If n and m denote the number of points in R where g is not continuous and not differentiable, respectively, then n + m is equal to ________.

Step-by-step solution

The given function is f x = 3 1 - | x | 2 i f | x | ≤ 2 0 i f | x | > 2 By using the definition of modulus function, we have x =       x , x ≥ 0 - x ,   x < 0 and also, we know that if x ≤ a ,   ⇒   - a ≤ x ≤ a and if x > a ,   ⇒   x < - a   o r   x > a , ⇒ f x = 3 1 + x 2 , - 2 ≤ x ≤ 0 3 1 - x 2 , 0 < x ≤ 2 0 , - 2 > x   o r   x > 2 Now, f x - 2 = 3 1 + x - 2