Use the definition of “f (x) is O(g(x))” to show

Elma Wilson

Elma Wilson

Answered question

2021-11-15

Use the definition of “f (x) is O(g(x))” to show that
2x+17 is O(3x)

Answer & Explanation

Witionsion

Witionsion

Beginner2021-11-16Added 19 answers

We have:
Given: O(3x), thus g(x)=3x in the definition of the Big-O Notation
f(x)=2x+17
When x>1, we have the property 3x>2x
Since 32=9 and 33=27, we obtained the property 3x>17 when x>2
For the purpose of simplicity, we will use k=2 and so use x>2.
|f(x)|=|2x+17|
|2x|+|17|
=2x+17
<3x+17
<3x+3x
=2|3x|
As a result, we must select C to be at least 2. Let us now consider C=2.

By the definition of the Big-O-notation, f(x)=O(3x) with k=2 and C=2

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