I have to prove:
$O(x)+O(x^2)=O(x^2)$ for $x\to\infty$ where "O" is the Big-O-Notation
Specific functions are no problem for me, but I have some difficulties with this general form. But nevertheless I tried the following:
$O(x)$ means $|f_1(x)|\leq |C_1 \cdot g_1(x)|$ with $g_1(x)=x$, and $O(x^2)$ means $|f_2(x)|\leq |C_1 \cdot g_2(x)|$ with $g_2(x)=x^2$ So we get $C_1 x + C_2 x^2 \leq (C_1+C_2) x^2$, which is $O(x^2)$ with $C_3=C_1+C_2$.
Is this start ok or its a big fault? Any hint would be nice.