Functions create confusion

Algebra Level 4

Suppose 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^2 for x0x \not= 0. Then f(2)=A\large f(-2) = {A}. Find 100A\large \left \lfloor {100 A} \right \rfloor, where \lfloor \cdot \rfloor denotes the floor function.

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