Suppose two function machines are hooked up in a sequence, so the output chute of machine \( g \) empties into the inpu 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 \( f(x)=2 x \) and \( g \) is the "add 5 " function \( g(x)=x+5 \). Suppose the doubling and the "add 5 " machines are coupled in reverse order to define the composition of \( g \) and \( f \) given by \( G(x)=g(f(x)) \). Then \( G(4)=g(f(4))=g(2 \times 4)=g(8)=8+5=13 \). Evaluate \( g(f(x)) \) for \( x=0,1,2 \), and 3 .