made easy test series

Question

Let f (n) = Ο(n), g(n) = Ο(n) and h(n) = θ(n).

Then [f (n) . g(n)] + h(n) is _______.

a.Ω(n)

b.Ο(n)

c.θ(n)

d.None of these

Comments

Is it C?

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if
f(n) = n which is O(n)
g(n) = n which is  O(n)
h(n) = n

$f(n)*g(n) + h(n) = (n^2 + n) = O(n^2).$

if
f(n) = 1 which is O(n)
g(n) = 1 which is  O(n)
h(n) = n

$f(n)*g(n) + h(n) = (c + n) = omega(n).$

Hence (A) is the correct choice!

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yes , answer should be a ie omega(n) but given answer is c

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Manu Sir I understood your solution but can we take f(n)=1 ? I thought f(n) should be a function of 'n' and can't be some constant.

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yes, we can, because we can have a function as $f(n) = n^0$, right? we only need to consider that f(n) is O(n).
(or)

a more practical example, there is a C program which takes n as input and print it, that's all.

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Okay...thank you Sir

And another thing..can we consider f(n)=1/n for such type of  problems  though it is practically impossible for any program?

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yes, we can consider 1/n also and in fact if f(n)=1/n then f(n) is O(1).

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Okay thanks :)