Showing posts with label functions math. Show all posts
Showing posts with label functions math. Show all posts

Saturday, February 23, 2013

Explanation of Functions Math

Introduction for explanation of function in math:

Before giving the explanation of the function in math, we have to know, what is function in math? The function is nothing that gives the result for the given argument. The argument is also know and element of the function from the given set. Function is associated with domain and co domain. The element exists in domain is also exactly one element in co domain. I like to share this Jointly Distributed Random Variables with you all through my article.


Pre-requisite for explanation of function in math:

Constant and Variable:

The value will not be changed during the mathematical process is called constant. The value will be changed during the mathematical process is called variable.

Interval:

The subset of real number is called interval

Neighborhood.

In a number line the neighborhood of a real number is defined as an open interval of very small length.

Independent / Dependent Variable:

A variable is an independent variable when it has any arbitrary value. A variable is said to be dependent when its value depends on other variables.

Cartesian product:

The Cartesian product of the two sets A and B is denoted by A x B and is denoted as

Let A={ a1,a2,a3} B={b1,b2}

A x B={ (a1,b1),(a1,b2)(a2,b1)(a2,b2)(a3,b1)(a3,b2)}


Explanation of function in math:


A function is a special type of relation. If no two ordered pairs have same first element and deferent second element, the relation is called function. If two ordered pairs have same first element and deferent second element, the relation is called not a function. If the element x in the set A is associated with element x in the set B is called image of the function. The set of images is called range of the function. If the range of function in not equal to the co domain, those functions are called mapping. Understanding Derivative Problems is always challenging for me but thanks to all math help websites to help me out.


Types of functions for explanation in math:


1. Identity function:

A function from a set A to the same set A is said to be an identity

2. Inverse of a function:

To define the inverse of a function f i.e. f-1 (read as ‘f inverse’), the

function f must be one-to-one and onto.

3. Constant function:

If the range of a function is a singleton set, the function is called a

constant function.

4. Linear function:

If a function f : R ? R is defined in the form f(x) = ax + b then the function

is called a linear function. Here a and b are constants.

5. Polynomial function:

If f : R?R is defined by f(x) = an xn + an - 1 xn - 1+ …+ a1x + a0, where

a0, a1,…, an are real numbers, an?0 then f is a polynomial function of degree n.