Thus, as x→0 (from the left), F(x) →(-B)/(-2) = B/2
Also, as x→0 (from the right), Ax + B → B, therefore, B = B/2. B = 0 is the only value such that the limits of x as it approaches zero from the left and right are the same – the condition of continuity there.
As x → 4 (from the right), 2x2 → 32, therefore, A = 8
The answer is A = 8 and B = 0.