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

 Dec 24, 2019
 #1
avatar+355 
+2

The first condition should be followed for numbers that are lower than or equal to 1.

The second condition should be used for numbers that are higher than 1.

Since f^-1(-3) follows the first condition, do 2-(-3)=5.

Similarly, since f^-1(0) also follows the first condition, do 2-0=2.

Since f^-1(3) follows the second condition, as 3 is bigger than 1, do 2*(3)-3^2 = 6-9 = -3

 

5 + 2 - 3 = 4

 

The answer is 4. 

 Dec 24, 2019
 #2
avatar+109563 
+1

f-1 (-3)     means that  f ( x)  =  - 3

This happens when x  =  3

So  f-1 ( -3)   = 3

 

f-1 (0)  means that   f(x)  =  0

This happens when x = 2

So  f-1(0)  =  2

 

f-1(3)   means  that  f(x)  = 3

This happens when  x = -1

So   f-1(3)  = -1

 

So

f-1 (-3)   + f-1(0) +  f-1(3)  =

 

     3       +     2       +  (-1)  =

 

4

 

 

 

cool cool cool

 Dec 25, 2019

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