For example, the function in part $($b$)$ is $O(x^2).$ We can choose witnesses $C=1001$ and $k=1$ so that

we'll have $x^2+10001001x^2$ when $x>1.$ Note that this choice of witnesses is not unique$-$there

are infinitely many other choices. For example, we could pick $C=2$ and $k=31$ so that we'll have

$x^2+10002x^2$ when $x>31.$