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Let f and g be functions of natural numbers given by f(n) = n and g(n) = n². Which of the following statements is/are TRUE?

1. f ∈ O(g)
2. f ∈ Ω(g)
3. f ∈ o(g)
4. f ∈ Θ(g)

Correct answer: f ∈ O(g)

Solution

The statement f ∈ O(g) is true because the function f(n) = n grows at a rate that is asymptotically less than or equal to the growth rate of g(n) = n², meaning there exists a constant C such that f(n) is bounded above by C * g(n) for sufficiently large n.

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