ভিডিও কনটেন্ট

ফাংশন ও ফাংশনের লেখচিত্র । উচ্চতর গণিত ১ম পত্র | Domain and range

মনির হোসেন ১৪ জানুয়ারি,২০২১ ৩৯ বার দেখা হয়েছে লাইক কমেন্ট ৫.০০ রেটিং ( )

Function (mathematics)

From Wikipedia, the free encyclopedia
Jump to navigationJump to search

In mathematics, a function[note 1] is a binary relation between two sets that associates every element of the first set to exactly one element of the second set. Typical examples are functions from integers to integers, or from the real numbers to real numbers.

Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the 19th century in terms of set theory, and this greatly enlarged the domains of application of the concept.

A function is a process or 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 (possibly the same set), the codomain of the function. It is customarily denoted by letters such as fg and h.[1]

If the function is called f, this relation is denoted by y = f(x) (which reads "f of x"), where the element x is the argument or input of the function, and y is the value of the function, the output, or the image of x by f.[2] The symbol that is used for representing the input is the variable of the function (e.g., f is a function of the variable x).[3]

A function is uniquely represented by the set of all pairs (xf(x)), called the graph of the function.[note 2][4] When the domain and the codomain are sets of real numbers, each such pair may be thought of as the Cartesian coordinates of a point in the plane. The set of these points is called the graph of the function; it is a popular means of illustrating the function.

Functions are widely used in science, and in most fields of mathematics. It has been said that functions are "the central objects of investigation" in most fields of mathematics.[5]

মতামত দিন
সাম্প্রতিক মন্তব্য
মোঃ তারেকুন্নবী ICT4E জেলা অ্যাম্বাসেডর
১৫ জানুয়ারি, ২০২১ ০১:৩৭ পূর্বাহ্ণ

লাইক ও পূর্ণ রেটিংসহ আপনার জন্য শুভকামনা রইলো। আমার আপলোডকৃত কনটেন্ট দেখে আপনার মূল্যবান মতামত ও পরামর্শ দেওয়ার জন্য অনুরোধ করছি।