Assume you are given asymptotically positive functions f and g such that f(n) = O(g(n)). For each of the following statements, either prove that it is true, or give a counterexample demonstrating that it is false:

1. f(n)² = O(g(n)²).

2. 2^f(n) = O(3^g(n)).

3. f(n) = (f(n/2)).

4. g(n) = (f(n)).