Suppose you are given asymptotically positive functions f and g. For each of the following statements, either prove that it is true, or give a counterexample demonstrating that it is false: 1. If f(n) = O(g(n)) then 2f(n) = O(29(n)). 2. If f(n) = 0(g(n)) then f(n)2 = 0(g(n)2). 3. If f(n) = O(g(n)) then fin) = (g()). 4. f(n) = O(f(n 1))