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\($f^{-1}(-3)+f^{-1}(0)+f^{-1}(3)$\)
+128460 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
