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2 function machines, arranged so that, the output from the top machine, with rule labeled, L, of x, becomes the input for the bottom machine, with rule labeled, r, of x. Lacey and Richens each have their own personal function machines. Lacey’s machine, , squares the input and then subtracts one. Richens’s function machine, , adds to the input and then multiplies the result by three.

  1. Write the equations that represent .

  2. Lacey and Richens decide to connect their two machines, so that Lacey’s output becomes Richens’s input. If  is the initial input, what is the eventual output?

  3. What if the order of the machines was changed? Would it change the output? Justify your answer.

    Try computing the result for if the order is reversed.