Answer:
1. f(n) = 6n² + 3
We can see that f(n) is a polynomial of degree 2. Therefore, f(n) is O(n²) by definition of Big-O.
2. f(n) = n² + 17n + 2
Again, f(n) is a polynomial of degree 2. Therefore, f(n) is O(n²) by definition of Big-O.
3. f(n) = n³ + 100n² + n + 10
Since f(n) is a polynomial of degree 3, we can say that f(n) is O(n³) by definition of Big-O.
4. f(n) = logn + n
We can see that n grows faster than logn. Therefore, we can say that f(n) is O(n) by definition of Big-O.
5. f(n) = logn + nlogn + n³ + n!
We can see that the term n! grows much faster than any other term in the expression. Therefore, we can say that f(n) is O(n!) by definition of Big-O.