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Let f, g : Z → Z be defined as follows: ? f(x) = {x +...

  1. Let f, g : Z → Z be defined as follows:

    ? f(x) = {x + 1 if x is odd; x - 1 if x is even}, g(x) = {x - 1 if x is odd; x + 1 if x is even}.

  2. Describe the functions fg and gf. Then compute the orders of f, g, fg, and gf.

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