You cannot find specific values of A and B in (2) and the problem does not ask you to. Saying that the function
is continuous at x= 1 tells you that the two one sided limits are equal: A- B= 3. Saying that the function is
not continuous at x= 2 tells you that the two one side limits there are
not equal. From the left, the limit is 3(2)= 6. From the right, it is 4B- A and we can only say that
. From, A- B= 3, we get B= A- 3 and we can put that into the inequality: A- B= A- (A- 3)[/tex] which reduces to just 3. Certainly 3 is NOT equal to 6 so the only "condition" we need for A and B is that A- B= 3. What the value of the function
is at x= 2 depends upon what A and B individulally are. For example, if we take A= 3, then B= 0 satisfies A- B= 3. In that case, the value of f(2) is 4B- A= -3. But we could also take A= 4, B= 1. That also satifies A- B= 3. Now the value of f(2) is 4B- A= 4-4= 0.