Here are some problems that about algorithms.

Let f(n) and g(n) be asymptotically positive functions (that is, f(n) and g(n) are positive when n is sufficiently large). Prove or disprove each of the following conjectures. (a) f(n) = 0(g(n)) implies 2f(n) = 0(29(n)) (b) f(n) = 0(f(n))2)