how can be prove that $\max(f(n),g(n)) = \Theta(f(n)+g(n))$
how can be prove that $\max(f(n),g(n)) = \Theta(f(n)+g(n))$
though the big O case is simple since $\max(f(n),g(n)) \leq f(n)+g(n)$
edit : where $f(n)$ and $g(n)$ are asymptotically nonnegative functions.
Hint...: $2 + 100 \le 100 + 100$
For the sake of completeness:
Use the fact that: $\max(f,g) \le f + g \le 2\max(f,g)$ when $f,g$ are non-negative