GATE | CS 2022 | Question 11

Which one of the following statements is TRUE for all positive functions f (n)?

(A)

, when f (n) is a polynomial

(B)

(C)

, when f (n) is an exponential function

(D)

Answer:(A)
Explanation:

Option A: It always holds because if we square the input variable, then the highest order in the polynomial will also get squared.

Option B: It is not true in cases when f(n) is a polynomial function.

Option C: An exponential function may be increasing or decreasing, so this condition may not always be true.

Option D: It need not be true for a function that is decreasing.

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