Big-O Practice. For each of the following sub-parts, say whether f is O(g), Big Theta(g), Big Omega(g), or none of the above. Justify your answers. Remember, "log" denotes base-2 log by default in this course.

a. f(n) = 2^n; g(n) = 4^(sqrt(n))

b. f(n) = log(n); g(n) = log(n^2)

c. f(n) = (n(n-1)/2); g(n) = n^2 +2n

d. f(n) = n^(log(n)); g(n) = (logn)^n

e. f(n) = 2^(sqrt(n)); g(n) = n^(log(n)^2)

f. Given f = O(g), f and g are positive.

Prove: f^2= O(g^2)