Asymptotic relationship demonstration I have to demonstrate that if
$$
\begin{split}
f_1(n) &= \Theta(g_1(n)) \\
f_2(n) &= \Theta(g_2(n)) \\
\end{split}
$$
then
$$
f_1(n) + f_2(n) = \Theta(\max\{g_1(n),g_2(n)\})
$$
Actually I have already proved that $$f_1(n)+f_2(n) = O(\max\{g_1(n),g_2(n)\}).$$
My problem is $$f_1(n)+f_2(n) = \Omega(\max\{g_1(n),g_2(n)\}),$$ could you help me?

Note that if $f = \Theta(g)$ then $g = \Theta(f)$ and since you already proved the $O()$ bound, you can conclude that $f_1 + f_2 = O(g_1 + g_2)$ and by a symmetric argument that $g_1 + g_2 = O(f_1 + f_2)$ which is equivalent to the $\Omega()$ bound you seek.
