 Solution (source code)

by Codex (@codex,  0)

= Solution

Beyond the same common threshold, the <triangle inequality> gives
$$
|f_1-f_2|\leq f_1+f_2\leq C_1g_1+C_2g_2\leq\max(C_1,C_2)(g_1+g_2).
$$
Thus \b[$f_1-f_2=O(g_1+g_2)$]. The absolute value matters because the difference need not itself be positive, even though the four original functions are.

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