Math Homework Help: What are the conditions to make the Piecewise function continuous

f(x) = {Ax - B, when x≤1
{ 3x, when 1 {Bx² - A, when 2≤x

What are the conditions of A and B to make the function continuous at x=1 and discontinuous at x=2?

Ax – B = 3 when x = 1
Bx² – A = 6 when x = 2

A – B = 3
–A + 4B = 6 {Add equations}
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3B = 9,
B = 3

A – 3 = 3

A = 6

So, when x=1, we want Ax-B=3x. So A-B=3. And we want at x=2, 3x not equal to Bx^2 - A. Then, 6 is not equal to 4B - A. From the first part we can get B - A = -3 and then we can apply that to 3B + B - A is not equal to 6 to get 3B - 3 or 3(B - 1) is not equal to 6 and thus B - 1 is not equal to 2 and B is not equal to 3.