proof - Using the formal definition of Big-Oh to prove the following statements

Question

f(n) and g(n) are non-negative functions. With that being said, I'm trying to prove the following statement using the formal definition of big O f(n) <= c x g(n).

If f(n) ∈ O(d ? g(n)) for some d ∈ R>0, then f(n) ∈ O(g(n))

How would this look as a proof? I don't even know where to start. I was thinking that n would 1 and the value for both of the c's would be 1 as well.

question from:https://stackoverflow.com/questions/66049874/using-the-formal-definition-of-big-oh-to-prove-the-following-statements

Answer 1

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