Are big O and big Omega mutually exclusive

Question

Are big O and big Omega exclusive? In the sense for a function f(n) can g(n) be both big omega and big O of that function? For example lets say f(n) = n+nlog(n) and g(n) = sqrt(n)+ n^2. I know for sure that f(n) = O(g(n)) because n^2 is going to dominate all of the other functions. But would there be a case where f(n) = big Omega (g(n))? Or would there be another example that could show a function g(n) be a big-O and a big-Omega of a function f(n)?

Answer 1

They are not mutually exclusive. An example can be f(n)=g(n). In this case, we will say that f(n) is big Theta of g(n) see this under: 'Big Theta notation' for more information