Let f(n) = n lg n and g(n) = n^2. (a) Show that f(n) is 0(g(n). (b) Argue that lg n/Squareroot n is O(Squareroot n). (c) Justify that g(n) is not O(f(n)). (d) Exhibit that f(g(n)) is O(g(f(n)). (e) Prove that g(f(n)) is not O(f(g(n)).
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