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Suppose that g 1 (n) is O(h 1 (n) ) and g 2 is O(h 2 (n)) , and let g(n) = g 1 (n)g

Suppose that g₁(n) is O(h₁(n)) and g₂is O(h₂(n)), and let g(n) = g₁(n)g₂(n) and h(n) = h₁(n)h₂(n).

Show that g(n) is O(h(n)). Prove this fact using only the definition of big-O.

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