foundations for functions algebra

Function - We consider two sets A and B. We form the Cartesian Product, we form relations. From all the relations, we can select a few which satisfy the rule that each element of the set A is related to only one element of the set B. When a relation satisfies this rule, it is called a fuc..

We consider two sets A and B. We form the Cartesian Product, we form relations. From all the relations, we can select a few which satisfy the rule that each element of the set A is related to only one element of the set B. When a relation satisfies this rule, it is called a fuction. In this chap..

Function - Any relation on A x B in which (i) no two second elements have a common first element and (ii) every first element has a corresponding second element is called a function.Any relation on A x B in which (i) no two second elements have a common first element and (ii) ev..

Summary Relations and Functions - A pair of objects, written in a specified order is called an ordered pair . A pair of objects, written in a specified order is called an ordered pair . For the ordered pair (a,b), a is called the first element and b, the second element. The ordered pairs ..

Representation of a Function - A function can be represented by the following methods:A function can be represented by the following metho..

A function can be represented by the following methods: (i) An arrow diagram. (ii) Cartesian graph. (iii) Set-builder notatio..

A function f : A g B is said to be a constant function, if ..

Let f : A g B and g : B g C be two functions. Let h: A g C be function such that h(x) = g(f(x)) h is called the composite of f and g, denoted by h = g o f. i.e., (g o f) (x) = g (f(x..

Relations and Functions - In our daily life, we come across many relations such as father-son, brother-sister, teacher-student and many more. In mathematics too, we come across relations such as . A is a subset of B . line l is parallel to line m . number m is less than number n . In all ..

In our daily life, we come across many relations such as father-son, brother-sister, teacher-student and many more. In mathematics too, we come across relations such as . A is a subset of B . line l is parallel to line m . number m is less than number n . In all these, we notice..