Doubt

Question

Consider f (n), g(n) and h(n) be function defined as follows:

Which of the following represents correct asymptotic solution for f (n) + [g(n) × h(n)]?

A .  Omega(n^3)

B.   O(n^4)

C.   Theta(n^4)

D.   O(n^3)

What should be the correct way of solving such questions ?

Comments

But according to made easy answer is A

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I don't think so

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Let k(n) = g(n) * h(n)

Then k(n) = O(n^4)

Now, here f(n) = omega(n^3) that means

f(n) is asymptotically greater than n^3.

Now, since k(n) is asymptotically positive we will have

f(n) + k(n) is asymptotically greater than n^3

Thus f(n) + k(n) is omega(n^3)

I hope this helps.

Answer 1

Yeah (A) will be correct answer because f(n) is omega of n^3 which means f(n) >= (n^3) ,for that i can take any value greater than (n^3) and this is also adding with other function ,for that only omega of (n^3) can satisfy .

In option (B) is O (n^4) means <= n^4,what if i take f(n) as n^5,so (B) will be wrong answer