f(g(x)) ≠ g(f(x)): the innermost machine runs first, which is the opposite of the reading order and is exactly why the error is so common. With f(x)=x^2-3 and g(x)=2x+1, f(g(3))=46 while g(f(3))=13 — and 13 is always on the page as the reversed-composition distractor.