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Give a formal proof for: f(n) O(g1(n)) and h(n) O(g2(n)) f(n) + h(n) O(MAX(g1(n), g2(n))).

Give a formal proof for:
f(n) O(g1(n)) and h(n) O(g2(n)) f(n) + h(n) O(MAX(g1(n), g2(n))).

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