Find the values of a and b for which the function f defined below is continuous at x=4. f(x)={x-4/|x-4| +a,x≤4 a+b,x=4 x-4/|x-4| +b,x≥4 Share with your friends Share 0 Manbar Singh answered this LHL = limx→4- fx = limx→4- x-4x-4 + a = limx→4-x-4-x-4 + a = limx→4--1 + a = a - 1RHL = limx→4+ fx = limx→4+ x-4x-4 +b = limx→4+x-4x-4 +b = limx→4+1 +b=b+1Now, f4 = a + bSince, f is continuous at x = 4So, LHL = RHL = f4⇒a - 1 = b + 1 = a + b⇒a - 1 = a + b .....1 and b + 1 = a + b⇒b = -1 and a = 1 1 View Full Answer
