1.Suppose f(n) = 100n + log n and g(n) = n + (log n)^2

Which of the following holds?

f(n)=O(g(n))

g(n)=O(f(n))

f(n)=O(g(n)) and g(n)=O(f(n))

ANS: g(n) = O(f(n))

2.Suppose f(n)=n log n and g(n)=10n log(10n)

Which of the following holds?

f(n)=O(g(n))

g(n)=O(f(n))

f(n)=O(g(n)) and g(n)=O(f(n))

ANS: f(n)=O(g(n)) and g(n)=O(f(n))

I know what the answer for each question, but I have not got yet how can I find out the answer.

Could you explain me how to solve them, please?

Thank you in advance.