Suppose two function machines are hooked up in a sequence, so the output chute of machine g empties into the input hopper of machine f. Such a coupling of machines, which is defined if the range of g is a subset of the domain of f, is called the composition of f and g and can be written F(x) = f(g(x)). Suppose f is the doubling function f(x) = 2x and g is the "add 6" function g(x) = x + 6. Then F(4) = f(g(4)) = f(4 + 6) = f(10) = 2x 10 = 20. Evaluate f(g(x)) for x = 0, 1, 2, and 3.

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