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?
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
+7 
