Big O, Big Omega, and big Theta. Please provide an explanation of how you got the answer. I have already solved the problems, but I want to make sure I am correct.

(10 pts) Use O, , or to relate each of the following pairs of functions. In particular, you need to write your answer as f(n) E 0(g(n), f(n) E (g(n)), or f(n) E (g(n)). In case f(n) E (g(n)), you will not receive credit if you write f(n) E 0(g(n)) or f(n) E (g(n)), although both are implied by f(n) (g(n)). IR (a) f(n)-200x (log n), g(n)-0.0001 (b) f(n) 1.0001", g(n) n2. . i-l ! (d) f(n) 3 x n!, g(n) (3 x n! (e) f(n)-noo, g(n)- 100 n0.01