Big-O notation question

**bokasoka** · June 21st 2010, 07:09 PM

hi guys,
can someone pls explain big-o notation to me in easy to understand way with an easy example?? I am trying to understand it by reading my textbook but i am not getting it at all. It uses the following example: show that f(x) = x^2 + 2x + 1 is O(x^2)

My first question is, what value of x do i start with?? i dont know how one chooses a value of x to start with. in the book, it starts with x > 1. I dont understand how they came up with 1 instead of 2, 3 or any other number.

if someone could please answer my question and also explain the big-o notation in an easy to understand way with an example, it would be great. thanks a lot in advance! i really appriciate it.

**CaptainBlack** · June 21st 2010, 08:36 PM

Originally Posted by bokasoka

hi guys,
can someone pls explain big-o notation to me in easy to understand way with an easy example?? I am trying to understand it by reading my textbook but i am not getting it at all. It uses the following example: show that f(x) = x^2 + 2x + 1 is O(x^2)

My first question is, what value of x do i start with?? i dont know how one chooses a value of x to start with. in the book, it starts with x > 1. I dont understand how they came up with 1 instead of 2, 3 or any other number.

if someone could please answer my question and also explain the big-o notation in an easy to understand way with an example, it would be great. thanks a lot in advance! i really appriciate it.

$f(x) \in O(g(x))$

means that for big enough $\displaystyle x$ : $|f(x)|$ is less than (or equal) some fixed multiple of $\displaystyle g(x)$ . This means that there exists an $x_0$ such that for all $x\ge x_0$ , and a $k>0$ :

$|f(x)|\le k g(x)$

In the case of your example for all $x \ge 1$ ; $x^2\ge x$ and $x^2 \ge 1$ . Hence for all $x \ge 1$

$|f(x)|=f(x)=x^2+2x+1\le x^2+2x^2+x^2=4x^2$

Hence $f(x) \in O(x^2)$ (using $x_0=1,\ k=4$ )

CB

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