Question

Find the relationship between a and b so that the function f defined by f(x) = {(ax + 1, if x ≤ 3), (bx + 3, if x > 3) is continuous at x = 3.

Answer 1

Also, f(3) = 3 a +1 [since f(x) = ax + 1] 

Since, f(x) is continuous at x = 3. 

∴ LHL = RHL = f(3)

⇒ 3a + 1 = 3b + 3 

⇒ 3a = 3b + 2 

⇒ a = b + 2/3