In Asymptotic Analysis, Show That :- O( f(n) + g(n) ) = O( max{ f(n) , g(n) } ) [closed]

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O represents Big-O.

O(g) : { f| f is non negative function

             there exists c,m where c and m are any constants

             such that f(n) <= cg(n) for all n >= m }

           Show That :- O( f(n) + g(n) ) = O( max{ f(n) , g(n) } ) .

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This follows from max{f(n), g(n)} <= f(n) + g(n) <= 2*max{f(n), g(n)}.