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Suppose that g(x) = f^-1(x). If g(-15) = 0, g(0) = 3, g(3) = 9, and g(9) = 20, what is f(f(9))?

 Oct 1, 2019
 #1
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Suppose that g(x) = f^-1(x). If g(-15) = 0, g(0) = 3, g(3) = 9, and g(9) = 20, what is f(f(9))?

 

If g(3) = 9

Then the point  (3,9) is on the inverse

Then  because f-1 (x)  is the inverse of  g

Then the point   (9,3)   is on f(x)

So   f(9)  = 3

 

Then f(f(9) )   =   f(3)

But g (0)  = 3   

Then the point  (0,3)  is on g(x)  = f-1(x)

Which means that the point  (3,0)  is  on the graph of f(x)

 

So

 

f(f(9))  = f(3)   =  0

 

 

cool cool cool

 Oct 2, 2019
edited by CPhill  Oct 2, 2019

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