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Suppose f(x)f(x)f(x) is a rational function such that 3f(1x)+2f(x)x=x23 f \left(\dfrac{1}{x} \right) + \dfrac{2 f(x)}{x} = x^23f(x1)+x2f(x)=x2 for x≠0x \not= 0x=0. Then f(−2)=A\large f(-2) = {A}f(−2)=A. Find ⌊100A⌋\large \left \lfloor {100 A} \right \rfloor⌊100A⌋, where ⌊⋅⌋\lfloor \cdot \rfloor⌊⋅⌋ denotes the floor function.
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