how to prove O(max{ f (n),g(n)}) = O( f (n)+g(n))? : I find a rule about algorithms for analysis.
    

    O(max{f(n),g(n)}) = O(f(n)+g(n)) 

how to prove it？
   I know 
    

    max{f(n),g(n)} <= f(n)+g(n) <= 2 * max{f(n),g(n)}

   thus 

    max{f(n),g(n)} is O(f(n)+g(n))
    max{f(n),g(n)} is O(max{f(n),g(n)})
    f(n)+g(n)      is O(max{f(n),g(n)})

   then? 