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# I actually need hellp

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Let F be defined by

$$$f(x) = \left\{ \begin{array}{cl} 2-x & \text{ if } x \leq 1, \\ 2x-x^2 & \text{ if } x>1. \end{array} \right.$$$

Calculate$$f^{-1}(-3)+f^{-1}(0)+f^{-1}(3)$$

Feb 14, 2020

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First

We need to find which function outputs   -3

2 - x  = -3                                                      2x - x^2  =  -3

x = 5    no good....x  must be ≤ 1                  x^2 - 2x - 3  = 0

(x - 3) ( x + 1)  = 0

x  = 3  is the  good solution here  because  x > 1

So  f-1(-3)  = 3

Next

We need to  find out  which function outputs  0

2- x  = 0                                                            2x  -x^2  =  0

2  = x     no good....x must be ≤ 1                     x (2 - x)  = 0

x = 2  is the good solution here

So  f-1 (0)  =  2

Finally

We need to find out which function  outputs 3

2 - x = 3

x = -1

good..... x is ≤ 1

So  f-1 (3)  = -1

So

f-1(-3)  + f-1(0)   + f-1(3)  =

3      +    2       -     1   =

4   Feb 14, 2020