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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 $f^{-1}(0)+f^{-1}(6)$.

 Aug 13, 2023
edited by IMVERYBADATMATHHELP  Aug 13, 2023
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f-1(0)

Set the first function  = 0  

0 = 3- x

-3 = -x 

x = 3      

So f(3) =  0

Which means  that f-1(0)  = 3

 

f-1(6)

Set the second function  =  6

-x^3 + 2x^2 + 3x  = 6

By inspection , x =  2  ..... no good....x must be  > 3

 

 

So set the first function =  6

6 = 3 - x

x = 3 - 6

x = -3

So f(-3) = 6

Which means that  f-1(6)  = -3

 

So

 

f-1(0)  + f-1(6)  =    3 + - 3 =  0

 

 

cool cool cool

 Aug 13, 2023

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