Asymptotic Notation: f(N)+g(N)=O(h(N))? f(N)*g(N)=O(h(N))?

[needhelp83]

Suppose f(N) = O(h(N)) and g(N) = O(h(N))

1. Is f(N) + g(N) = O(h(N))
2. Is f(N) * g(N) = O(h(N))

Justify answers

I am totally lost on these questions. ANY help would be greatly appreciated.

 

[wildman]

This is the Big-O Notation. It is involved in comparing the growth of one number-theoretic function with that of another. There is a sequence of these functions. For instance:

f_2 = log_2 n
.
.
.
f_{7.2} = n^2
f_{7.3} = n^3
.
.
.
f_{7.k} = n^k
.
.

Now answer these questions:

Does adding n^2 to n^2 change the level in the sequence?
How about multiplying? (different constants don't count)