Consider the function f(n) = 2n^3 + 5n^2 + 42. Use the definition of big-O to prove that f(n) elementof O(n^3). Consider the function g(n) = 12n^2 log n^2 + 6n + 42. Use the definition of big-O to prove that g(n) elementof O(n^2 log n^2). Consider again the function g(n) = 12n^2 log n^2 + 6n + 42. Use the definition of big-O to prove that g(n) is not in O(n)