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The entire graph of the function f(x) is shown below (f is only defined when x is between -4 and 4 inclusive). How many values of x satisfy f(f(x)) = 2?

 

 Jun 29, 2022
 #1
avatar+124676 
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f(f(x)) =  2(2x + 3) + 3  =    4x + 6 + 3    =  4x + 9

 

f(f(x))  = 2

 

4x + 9 =   2

 

4x  =  2 - 9

 

4x =  -7

 

x = - 7/4 

 

 

Proof

 

f  (-7/4)  = 2 (-7/4) + 3 =  -14/4 + 12/4  =    -2/4 = -1/2

 

f ( f(-7/4)) =   f(-1/2)  =  2 (-1/2) + 3   =   2

 

 

 

cool cool cool

 Jun 29, 2022

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