Let f(n) = n² log n and g(n) = n (log n)¹⁰ be two positive functions of n.…

PYQ GATE 2001

Let f(n) = n² log n and g(n) = n (log n)¹⁰ be two positive functions of n. Which of the following statements is correct?

  1. A.

    f(n) = O(g(n)) and g(n) ≠ O(f(n))

  2. B.

    f(n) ≠ O(g(n)) and g(n) = O(f(n))

  3. C.

    f(n) ≠ O(g(n)) and g(n) ≠ O(f(n))

  4. D.

    f(n) = O(g(n)) and g(n) = O(f(n))

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