Chapter 4, Problem 14R

Explanation of Solution

Given:

It is given that if $d\left(n\right)$ is $O\left(f\left(n\right)\right)$ then $ad\left(n\right)$ is $O\left(f\left(n\right)\right)$ for constant $a>0$ .

Big-Oh notation:

In big-Oh notation, let “f” and “g” be functions from the integers or the real numbers to the real numbers.

• It means that $\text{f}\left(\text{x}\right)$ is “$\text{O}\left(\text{g}\left(\text{x}\right)\right)$” if there are constants “C” and “k” such that,

$\left|\text{f}\left(\text{x}\right)\right|\le \text{C}|$