Question

What is the asymptotic upper bound (Big O) of f( n ), if f( n )= 7n + 10 log n +n log n +8?

Select one:
a. O(1)
b. O(n log n)
c. O( log n)
d. O( n )

Answer 1

The asymptotic upper bound for the function f(n) = 7n + 10 log n + n log n + 8 is O(n log n), as the term n log n grows faster than the others and determines the function's complexity.

Step-by-step explanation:

The function f(n) = 7n + 10 log n + n log n + 8 is a combination of linear and logarithmic terms. When analyzing the complexity of such a function for the purposes of Big O notation, we're looking for the term that grows the fastest as n becomes large. In this case, the term n log n grows faster than the other terms.

Thus, the other terms become negligible as n increases, and the asymptotic upper bound is determined by the fastest-growing term, which is O(n log n).