Its option 2.

f=O(n),g=O(n^2)

f+g=O(n^2)

f*g=O(n^3)

f=O(n),g=O(n^2)

f+g=O(n^2)

f*g=O(n^3)

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Given that:

$f = O(h)$ and $g =O(k)$

This implies that $f \leq c_1h$ and $g \leq c_2k$.

Let $c_3= max(c_1, c_2)$.

$f + g = c_1h + c_2k \rightarrow f + g = c_3(h + k) \rightarrow f + g \in O(h+k)$.

This is true since we can replace $c_1$ and $c_2$ by $c_3$ while still maintaining the upper bound.

The same logic can apply for $fg$ also.

$f = O(h)$ and $g =O(k)$

This implies that $f \leq c_1h$ and $g \leq c_2k$.

Let $c_3= max(c_1, c_2)$.

$f + g = c_1h + c_2k \rightarrow f + g = c_3(h + k) \rightarrow f + g \in O(h+k)$.

This is true since we can replace $c_1$ and $c_2$ by $c_3$ while still maintaining the upper bound.

The same logic can apply for $fg$ also.

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