GATE CS 2022 Set 1 — Question 11
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Question
Which one of the following statements is TRUE for all positive functions ?
Correct answer
(A) f(n²) = θ(f(n)²), when f(n) is a polynomial
Solution
Check each statement; a statement claimed for a class of functions is false as soon as one function in that class breaks it.(A) True. Let with leading coefficient . Then and , soa positive constant. Hence .(B) False. Take : , which is not .(C) False. Take : while , and , so .(D) False. Take the positive function : and , and , so .Answer: (A)
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