#1**+1 **

Need to be careful here

f^{-1} (-3) means that either

2 - x = - 3

x = 5 but this value isn't in the domain of the first function

or

2x - x^2 = -3 rearrange as

x^2 - 2x - 3 = 0 factor

(x- 3) ( x + 1) = 0

x = 3 or x = -1

Only the first value is in the domain of the second function

So... f^{-1}(-3) = 3

Likewise

f^{-1}(0) means that either

2 - x = 0

x = 2 not in the domain for the first function

or

2x - x^2 = 0 factor

x (2 - x) = 0

x = 0 or x = 2

Only the second value is in the domain of the second function

So ...f^{-1}(0) = 2

Lastly

f^{-1}(3) means that

2 - x = 3

x = -1

This value is in the domain of the first function

So....f^{-1} (3) = -1

So

f^{-1}(-3) + f^{-1}(0) + f^{-1} (3) = 3 + 2 + -1 = 4

CPhill Feb 12, 2019