CPM Homework Help : INT3 Problem 5-46

2 function machines, arranged so the output of the top, becomes the input of the bottom: Top, input, 3, rule, f, of, x, = 5, x, minus 3, output, unknown. Bottom, input, unknown, rule, g, of, x, = open parenthesis, x, minus 1, close parenthesis, squared, output, unknown. Two function machines, $f(x) = 5x - 3$ and $g(x) = (x - 1)^2$ , are shown at right.

Suppose $f(3)$ , not $x = 3$ , is dropped into the $g(x)$ machine. This is written as $g(f(3))$ . What is this output?
Answer (a):
$f(3) = 12$
so $g(f(3)) = g(12) = 121$
Using the same function machines, what is $f(g(3))$ ? Be careful! The result is different from the last one because the order in which you use the machines has been switched!
Answer (b):
$f(g(3)) = 17$