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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 1, 2020
 #1
avatar+21953 
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To find a value that satisfies  f( f(x) )  =  2

let's find the inverse of both sides:  f(x)  =  f-1(2).

 

To find the value of  f-1(2),  we need to find the x-value of the point that has a y-value of 2.

The point that has a y-value of 2 is (0,2), so the value of f-1(2)  is  0.

 

We now have:  f(x)  =  0.

Again finding the inverse, we have  x  =  f-1(0)

and the x-value that produces a y-value of 0 is -4 (because the point (-4,0) is on the graph.

 

This is the only solution.

 Jun 1, 2020
 #2
avatar+793 
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Thank you!!

AnimalMaster  Jun 1, 2020

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