If the function f(x) defined by f(x) = cases ax + 1 & if x 3 bx + 3 & if x > 3 cases is continuous at x = 3 , then (a - b) = ..........

Step-by-step solution

For the function f(x) to be continuous at x = 3 , the left-hand limit must be equal to the right-hand limit and the value of the function at x = 3 . _ x 3^- f(x) = _ x 3^+ f(x) = f(3) Evaluating the left-hand limit: _ x 3^- (ax + 1) = 3a + 1 Evaluating the right-hand limit: _ x 3^+ (bx + 3) = 3b + 3 Equating the limits: 3a + 1 = 3b + 3 3a - 3b = 2 3(a - b) = 2 a - b = 2 3 Answer: 2 3