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Concept of Mathematics

Concept of Mathematics
Function

The function is a relation that associates each element x of a set X, the domain of the function, to a single element y of another set Y the function.

The various types of functions are as follows: Many to one function.

One-to-one function.

Onto function.

One and onto function.

Constant function.

Identity function.

Quadratic function.

Polynomial function.

One to one function.

A function is one to one if no two elements in the domain of g correspond to the same element in the range of g.

  In other words, each u in the domain has exactly one image in the range. 

And, no v  in the range is the image of more than one u in the domain.

Onto function.

Onto function can be explained by considering two sets, Set X and Set Y,

which consist of some elements not empty. If for every element of Y,

there is at least one or more than one element mapping with X,

then the function is called onto function or surjective function.

Constant function.

A constant function is a linear function whose range contains only one element of a domain.

Identity function.

The function f is called the identity function if every element of set X has an image on itself. 

Quadratic function.

 Quadratic function is written in the form f(x) = ax2 + bx + c,

where a, b, and c are coefficient with a not equal to zero.

The graph of a quadratic function is a curve called a parabola.

Polynomial function.

polynomial function is a function that consists of only non-negative integer powers

or only positive integer exponents of a variable in an equation is called a quadratic equation.

 Sequence and series

 Sequence

A sequence is an arrangement of any objects or a set of numbers in a particular order followed by some rule. If b1, b2, b3, b4,………

Types of Sequences

Arithmetic Sequence.

An arithmetic sequence is a sequence of numbers that the difference of any two consective members of the sequence is a constant.

2,4,6,8,10….is an arithmetic sequence with have same common diff.

an=a1+(n−1)d is the formula of arithmetic sequence a1 is called 1st term and d is called common difference.

Sn=n2(a1+an) is the formula of the sum of the arithmetic sequence where a1 is 1st and a^n is called last term of the sequence.

Geometric Sequence.

A geometric Sequence. is a sequence that have the same common ratio is defined as that

if the division of any two consecutive no is always the same for example 2,4,8,16…..

for example 4/2=2 and 8/4=2

Harmonic Sequence.

the harmonic sequence is reciprocal of an arithmetic sequence, for example, 1/a,1/b,1/c..

The nth term of the Harmonic Progression (H.P) = 1/ [a+(n-1)d]

Where

a is the first term of A.P

d is the common difference

n is the number of terms in A.P

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