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Determine whether each of these functions is O(x2).a)

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 2E Chapter 3.2

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 2E

Determine whether each of these functions is O(x2).

a) f(x)=17x +11

b) f(x) = x2 + 1000

c) f(x) = x log x

d) f(x) = x4/2

e) f(x) = 2x

f) f(x) = ⌊x⌋•⌊x⌋

Step-by-Step Solution:

Step 1:  In this problem,we have to determine whether each of these functions is O(x2).

Step 2:

The definition for Big- O:

Let f and g be functions from the real numbers to the real numbers. Then f is O(g) if there are constants c and k

Such that                           

Let f and g be function from the integers or set of real numbers.For this condition we can say f(x) is O(g(x) if f(x) is O(g(x)) and f(x) is (g(x)).

If f(x) is O(g(x)) if and only if there are positive constant C1 ,C2, and k

                         C1|g(x)|  C2|g(x)|   where x>k

Step 3 of 3

Chapter 3.2, Problem 2E is Solved
Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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