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1. Let $f$ be defined by$$f(x) = \left\{ \begin{array}{cl} 3-x & \text{ if } x \leq 3, \\ -x^3+2x^2+3x & \text{ if } x>3. \end{array} \right.$$Calculate $$f^{-1}(0)+f^{-1}(6).$$

2. There are numbers A and B for which$$\frac A{x-1}+\frac B{x+1}=\frac{x+2}{x^2-1}$$for every number $$x\neq\pm1$$. Find A-B.

3.The greatest integer function, $$\lfloor x\rfloor$$, denotes the largest integer less than or equal to x. For example, $$\lfloor3.5\rfloor=3$$, $$\lfloor\pi\rfloor=3$$ and $$\lfloor -\pi\rfloor=-4$$. Find the sum of the three smallest positive solutions to $$x-\lfloor x\rfloor=\frac1{\lfloor x\rfloor}.$$ Express your answer as a mixed number.