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 \(f^{-1}(0)+f^{-1}(6)\).
I tried solving this...to find \(f^{-1}(0)\), then I'd need to find the x that makes f(x) equal to 0, right? So I solved both equations for 0, for 3-x, x=3. For \(-x^3+2x^2+3x\), x can be 0, -1, or 3. But after this, I don't really think I'm solving this correctly.. I just don't understand how to find the inverses of f(0) and f(6).
