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2 function machines, arranged so the output of the top, becomes the input of the bottom: Top, input, x, rule, f, of, x, output, unknown, which is Bottom, input, bottom rule, g, of, x, output, g of f of x = question mark.When you stack one function machine on top of another so that the output of the first machine becomes the input of the second machine, you create a new function, which is a composition of the two functions. If the first function is and the second is , the composition of the functions can be written as the composite function .

  1. The function machines and are stacked as shown at right. If is input at the top, what expression comes out of the bottom? That is, what is the composite function ?

    This is .

  2. Write an expression for the composite function .