Question 374571: suppose F(X)=AX+B, G(X)=BX+A,(A AND B INTEGERS), F(1)= 8, F(G(50))-G(F(50))=28 FIND THE PRODUCT OF A AND B.
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! f(1) = 8 implies that a+b = 8.
f(g(50)) - g(f(50)) = f(50b +a) - g(50a+b) =  .
From the very first equation, a+b-1 = 7, so that after substitution into the last equation above, (a-b)*7 = 28, or a-b = 4. So
a-b = 4, and
a+b = 8.
It follows that 2a = 12, or a = 6, by elimination. Then b = 2. Therefore a*b = 12.
BTW, just replace a by A, and b by B. :D
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