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. For how many values of $x$ is the function $y=\frac{x-2}{x^2-7x+10}$ not defined?
3. If $\sqrt{5 + x} + \sqrt{20 - x} = 7$, what is the value of $(5 + x)(20 - x)$?