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# Determine whether each of these functions is O(x2).a) ISBN: 9780073383095 37

## Solution for problem 2E Chapter 3.2

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

##### ISBN: 9780073383095

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