Possible Duplicate:
how can be prove that $\max(f(n),g(n)) = \theta(f(n)+g(n))$
How to prove $max(f(n),g(n)) = Θ(f(n)+g(n))$?
Possible Duplicate:
how can be prove that $\max(f(n),g(n)) = \theta(f(n)+g(n))$
How to prove $max(f(n),g(n)) = Θ(f(n)+g(n))$?
Let $h=\max(f,g)$. Then $f+g\le 2h$ and so $f+g=O(h)$. If $f$ and $g$ are positive, then $h \le f+g$ and so $h=O(f+g)$.