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.
thank you in advance
