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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 \(f^{-1}(0)+f^{-1}(6)\)

 May 8, 2021
 #1
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.....You'll need to find the inverse functions

 

for f(0)  you need inverse of    3-x    which is 3-x         f-1(0) = 3

 

for 6 you need to find when    -x^3  + 2x^2 + 3x  = 6       or when   f(?) = 6         this occurs at     ? = 2

 

 

3+2 = 5

 May 8, 2021

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