Show your work using the definition O() (Using the two constants etc). Let f(n) = O(g(n))...

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Question

Show your work using the definition O() (Using the two constants etc). Let f(n) = O(g(n))...

Show your work using the definition O() (Using the two constants etc).

Let f(n) = O(g(n)) and g(n) = O(h(n)).

Show that f(n) = O(h(n)).

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Answer 1

Answer #1

`Hey,

Note: Brother if you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

f(n)=O(g(n))

g(n)=O(h(n))

Using definition of big O

f(n)<=c1*g(n)-----eq1

Also,

g(n)<=c2*h(n)------eq2

f(n)<=c1*g(n)<=c1*c2*h(n)

So,

f(n)<=(c1*c2)*h(n)

c=c1*c2

So,

f(n)<=c*h(n)

So, we found a c=c1*c2

f(n)=O(h(n))

Kindly revert for any queries

Thanks.

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Answer 2

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