Define f (x)= array cl b - a x & , if x 2 array . and if _ x 2 f (x) exists, then a b =

Step-by-step solution

The limit _ x 2 f(x) exists if and only if the left-hand and right-hand limits at x = 2 are equal. For x For x > 2 , f(x) = a + 2b x , giving the right-hand limit _ x 2^+ f(x) = a + 4b . Setting these equal: b - 2a = a + 4b . This simplifies to -3b = 3a , and dividing both sides by 3b (since b 0 for the ratio to be defined) yields a b = -1 . Final answer: B