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Suppose the graph of y=f(x) includes the points  (1,5) (2,3)  and (3,1) .

Based only on this information, there are two points that must be on the graph of y= f(f(x)). If we call those points (a,b) and (c,d), what is  ab+cd?

 Mar 16, 2021
 #1
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f(1) = 5

f(2) = 3

f(3) = 1

 

Let  y = f(f(x))

 

When  x = 2,    y  =  f(f(2))  =  f(3)  =  1

 

When  x = 3,    y  =  f(f(3))  =  f(1)  =  5

 

So the points  (2, 1)  and  (3, 5)  must be on the graph of  y = f(f(x))

 

ab + cd   =   2 * 1  +  3 * 5   =   2 + 15   =   17

 Mar 16, 2021

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