Discrete Math Decreasing Function

Discrete mathematics i fall 2014 3 2 pg 216 7 find the least integer n such that f x is o xn for each of these functions.

Discrete math decreasing function. A function assigns to each element of a set exactly one element of a related set. Therefore implies is true and it is an increasing function. A function is decreasing over an open interval a b if f x 0 for all x a b. The idea is this.

Functions find their application in various fields like representation of the computational complexity of algorithms counting objects study of sequences and strings to name a few. Discrete mathematics functions. The graph of the function will look like the following. Instead of an infinite sequence for example.

Section 5 1 generating functions. In the above graph the function is increasing between the interval of 0 2. A function is increasing on a section if the graph of that section rises to the right. The value of is 0 and is 3 the value of is 1 and is 5.

B f x 3x3 logx 4 3x3 logx 4 3x3 x3 for x 1 3x3 logx 4 4x3. Therefore if the derivative of a function is always positive or always negative then the function must be one to one. Since f x 1 x 2 0 f x frac 1 x 2 0 f x x 2 1 0 f x f x f x is a decreasing function in its domain 0 0 infty 0 cup 0 infty 0 0. A function is decreasing on some interval of its domain if f a f b for all a b in that interval such that a b.

Therefore n 3. 2 3 5 8 12 ldots we look at a single function which encodes the sequence. A function is decreasing on a section if the graph of that section falls to the right. There is an extremely powerful tool in discrete mathematics used to manipulate sequences called the generating function.

Consider the function f x 1 x f x frac 1 x f x x 1. R r defined by p x 2x3 5 is one to one because p x 6x2 0 for any x r. According to the definition a function is decreasing on an interval if f left x 1 right ge f left x 2 right for any two points x 1 le x 2 thus a decreasing interval may also contain points where the function has a constant value. A function is decreasing in an interval for any and.