What is the growth of each of these functions multiple choic

What is the growth of each of these functions? (multiple choice)

What is the growth of the below function: f(n) = n 7 squareroot n + n log^4 n + 2/n theta(n log^4n) theta(nlogn) theta (n) theta (n 4 squareroot n) What is the growth of the below function: f(n) = n^3 + 2 squareroot n + logn^9 O(logn^9) O(squareroot n) O(n^3) ohm(n^3) c and d

Solution

f(n) = n*n^(1/7) + n(logn)^4 + 2/n
   = n^(1.14) + n(logn)^4 + 2/n

here
   n(logn)^4 > n^(1.14) > 2/n

so, Big-O : O(n(logn)^4) , option 1 is answer

f(n) = n^3 + 2n + log(n^9)

   here, n^3 is the largest tern in give function, so

   Big-O : O(n^3)

   option c is answer