If f(x) = cases x^2 - 1 & if x 2 x + 1 & if x < 2 cases , then _ x 1 f(x) + _ x 2 f(x) =

Step-by-step solution

For x 1 , since x _ x 1 f(x) = _ x 1 (x + 1) = 1 + 1 = 2 For x 2 , we evaluate the left-hand and right-hand limits. Left-hand limit at x = 2 : _ x 2^- f(x) = _ x 2^- (x + 1) = 2 + 1 = 3 Right-hand limit at x = 2 : _ x 2^+ f(x) = _ x 2^+ (x^2 - 1) = 2^2 - 1 = 3 Since the left-hand limit equals the right-hand limit, _ x 2 f(x) = 3 . The required sum is _ x 1 f(x) + _ x 2 f(x) = 2 + 3 = 5 . Answer: 5