Introduction to class of functions

Introduction to class of functions:

·         In mathematics, the function means that assigns element from one set into another set element. The sets may be sets of numbers, sets of points, and sets of objects.

·         All the function has to be to do is to assign some element from the second set to each element in the first set.

·         Function can be classified two groups. Algebraic function and transcendental functions.

Algebraic Class Function:

                           A function class which involves operations only of additon, subtraction, multiplication and exponents on an  independent variable x is called an algebraic function.

Three particular class of functions are:

Polynomials function:

                A function of the form a₀xⁿ+a₁x^n-1+a₂x^n-2+........an where n is a positive integer and a₀,a₁,a₂...an are real constants is called a Polynomials function of a x.

Rational functions:

                  A function class of the form f(x)/g(x) where f(x) and g(x) are polynomial in x is called rational functions.

Irrational functions:

                The functions involving radicals are called irrational functions.

 

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Transcendental Class Function:

                             The following different class of  transcendental function are given as,

·         Trigonometric functions, such as cos x, tan 3x

·         Inverse trigonometric functions ,such as sin^-1x, sec^-1x

·         Logarithmic functions: The correspondence x-->log x is a logarithmic functions.

Identity function:

·         The identity function maps each member of the domain onto itself. That is, if I is the identity function ,then for any x in the domain, I(x)=x

·         If we let y stand for I(x), then y=x. It is easy to see that if the domain of I is the set of real number ,then the graph of the identity function is the line y=x. The identity function receives its name because it is the identity for the operation of composition.

Even and odd function:

·         If f (x) is a function of x such that f(-x)=f(x) for the every x of of its domain ,then it is called an even function of x

·         If f (x) = cos (x) ,then f(-x)= cos (-x)=cos x so that f (x)=f (-x).Thus f(x)=cos x is a even function.

·         If f (x) is a function of a x such that f (-x)=-f (x) for every x of its domain, then it is called an odd function of x.