Max of functions are in big O of the sum of their individual big Os

$\max(f(n), g(n)) = O(f(n) + g(n))$

How do I prove this? Also I'd appreciate the markup being corrected, thanks.

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I've never seen the notation O(f(n),g(n)), what does it mean for you? –  Yuval Filmus Nov 14 '10 at 7:43
@Yuval Filmus: Thanks, that was an error. I've corrected it. –  Matt Joiner Nov 14 '10 at 7:46
You can use $\max(f(n),g(n)) \leq f(n) + g(n)$, given that both functions are non-negative.