(d) Show that (x 2 + xy + xlogy) 3 is O(x 6y 3 ).

(e) Show that x 5y 3 + x 4y 4 + x 3y 5 is (x 3y 3 ).

(f) Show that 3x 2 + x + 1 is (3x 2 ).

(g) Suppose that f(x), g(x), and h(x) are functions such that f(x) is (g(x)) and g(x) is (h(x)). Show that f(x) is (h(x)). (h) Show that if f1(x) and f2(x) are functions from the set of positive integers to the set of real numbers and f1(x) is (g1(x)) and f2(x) is (g2(x)), then (f1f2)(x) is ((g1g2)(x)).