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 8" function g(x) = x +8. Suppose the doubling and the "add 8" machines are coupled in reverse order to define the composition of g and f given by G(x) = g(f(x)). Then G(4) = g(f(4) = g(2 x 4) = g(8) = 8+ 8 = 16. Evaluate g(f(x)) for x = 0, 1, 2, and 3. g(f(0)) = g(f(1)) = g(f(2)) = | g(f(3)) =|

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