I have the following problem 

The solution I derived is $O(g(n))$ where $C = 1, n > 1$. Is this solution correct ?
I have the following problem 

The solution I derived is $O(g(n))$ where $C = 1, n > 1$. Is this solution correct ?
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No. Hint: Your solution ($\sqrt(n) = O(log(n + 3))$ in verbose means that $\sqrt(n)$ grows as most as fast as $log(n + 3)$ $\forall n > 1$