Question: If f is a function from a set A to itself, we can compose f with itself. We call the composition of f with

If f is a function from a set A to itself, we can compose f with itself. We call the composition of f with 

If f is a function from a set A to itself, we can compose f with itself. We call the composition of f with itself k times the k'th iterate of f, and write it f(k). (a) If f(x)=x+2, what is the function f()? (b) If i and j are any naturals, is it always true that (f))(k) is equal to flik)? Why or why not? (c) How should we define f (0)? Why?

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