Let f(x) = Ax - 2B^2 and g(x) = 2Bx, where B is nonzero. If f(g(1)) = 0, what is A in terms of B?
g(1) = 2 Bx = 2B
f (g(1)) = f (2B) = A (2B) - 2B^2 and we are told this = 0
2B^2 = A (2B)
2 B^2 /2B = A
A = B
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