1. Let f : Z ≥0 → Z ≥0 be an arbitrary function. Define the function g(n) = f(n) + 1. Prove that g(n) = O(f(n)) if and only if f(n) = Ω(1). 2. Fill in each blank in the following table with an example...

1. Let f : Z^≥0
→ Z^≥0
be an arbitrary function. Define the function g(n) = f(n) + 1. Prove that g(n) = O(f(n)) if and only if f(n) = Ω(1).

2. Fill in each blank in the following table with an example of a function f that satisfies the stated conditions, or argue that it’s impossible to satisfy both conditions: