Use the properties of Big-Oh, Big-Omega, and Big-Theta to prove that if f(n) = ( 3 n) and g(n) = (f(n)+7f(n) 2 +49 n), then g(n) 3 = (n 2 ). You may use the fact that n a = O(n b ) if and only if a b, where a and b are constants.

Please provide a formal proof using the properties such as reflexivity, antisymmetry, transitivity, etc...