Question

How do you find the values of 'a' and 'b' that make f(x) continuous everywhere given x2−4x−2 if x < 2, ax2−bx+3 if 2 < x < 3 and 2x−a+b if x≥3?

Answer 1

Since f is continuous everywhere, it must be continuous at x= 2 and 3.

Apply the rule of continuity at x=2,3 i.e Left hand limit=Right Hand Limit and get the values of a and b. Hope this helps.