How is it posible that $f + g \in O(f)$? I am confused how to do this question. Intuitively it doesn't even make sense how a function $f$ plus another function is in $O(f)$. How can I approach this question:
$$ 
n\log(n^7)+n^{\frac{7}{2}} \in O(n^{\frac{7}{2}}).
$$
We know the fact that $\log n < n$ and I tried factoring out the $n$ but I am stuck. Any hints would be appreciated, Thanks!

The easiest way is to take the limit: $\frac{n^{\frac{7}{2}}+7 n \log n}{n^{\frac{7}{2}}} \to_n 1$, hence these two functions are of the same order.  
