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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 \(f(f(x)) = 2\)?

 


Thank you so much!

 Jul 17, 2020
 #1
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f(x) = 2 ==> x = -3, 0, 3

f(f(x)) = 2 ==> f(x) = -3, 0, 3

f(x) = 3 ==> three solutions

f(x) = 0 ==> 1 solution

f(x) = -3 ==> two solutions

 

A total of \(\boxed{6}\) solutions.

 Jul 17, 2020

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