function rules on 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..

Real Function: A real valued function f : A to B or simply a real function 'f ' is a rule which associates to each possible real number x A, a unique real number f(x) B, when A and B are subsets of R, the set of real number..

Rules of Inequalities - But we have, If an inequality is multiplied by a negative number, the inequality gets reverse..

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..

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..

In this section, you will learn how so solve inequalities. "Solving" an inequality means finding all of its solutions. A "solution" of an inequality is a number which when substituted for the variable makes the inequality a true statemen..

A function can be represented by the following methods:A function can be represented by the following metho..

Summary - A function is a relation on A x B is which A function is a relation on A x B is which (i) no two second elements have a common first element. (ii) every first element has a corresponding second element. Every function is either one-one onto or one-one into or..

There is at least one element of B which has no pre-image. In above fig.(i) the function is one-one and into, while in fig.(ii) the function is many-one and into. For types of functions, the four arrow diagrams given for one-one and many-one are repeated for ONT..

Every element of the set B has at least one pre-image. In above fig.(i), the function is one-one and onto, while in fig.(ii) the function is many-one and on..