What does it mean when f(n) ~ Cg(n) for some constant C > 0?a.The order of growth of f(n) is g(n).b.The order of growth of f(n) is Cg(n).c.The order of growth of f(n) cannot be determined.d.Non of these asnwers are correcte.The order of growth of f(n) is C

All of the terms in a growth function contribute to the order of the function   A. True B. False

Consider the following functions.f1(n) = (log n)2023f2(n) = n2logn(nn)f3(n) = n3+ 7n2f4(n) = 2. 023nf5(n) = n log nf6(n) = n *3n2Now do the followings:a. Write a correct asymptotic upper bound for each of the above.b. Sort the functions in ascending order of their growth rate, assuming n is significantlylarge. Just write the sorted order, no need to show any simulation.

If f(n) = O(g(n)), which of the following statements is true?g(n) grows faster than f(n) as n increasesf(n) grows faster than g(n) as n increasesf(n) and g(n) grow at the same rate as n increasesNone of the above

For each of the following pairs of functions, indicate whether the first functionof each of the following pairs has a lower, same, or higher order of growth (towithin a constant multiple) than the second function.a. n(n + 1) and 2000n2 b. 100n2 and 0.01n3c. log 2 n and ln n d. log 22 n and log 2 n2e. 2n−1 and 2n f. (n − 1)! and n!

able 2.1 contains values of several functions that often arise in the analysisof algorithms. These values certainly suggest that the functionslog n, n, n log 2 n, n2, n3, 2n , n!are listed in increasing order of their order of growth. Do these valuesprove this fact with mathematical certainty?b. Prove that the functions are indeed listed in increasing order of their orderof growth.