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Algebra I: A Basic Course in Abstract Algebra by Rajendra Kumar Sharma, Sudesh Kumari Shah, Asha Gauri Shankar

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Chapter 3

Functions

Function is a commonly used word in everyday life having different meanings. But, in Mathematics, the concept of a function is very basic and is of fundamental importance. Moreover, it has a very specific meaning. In this chapter we define mathematically a function and their various types and study their properties in detail. Operation on functions, conditions of invertibility and computation of the inverse of an invertible function will also be discussed.

3.1 Definition and Representation

Definition 3.1.    Let A and B be two sets. A binary relation f from A to B is called a function (or mapping) from A to B if each element of A is related to exactly one element of B. In other words, f is a function from A to B if for each ...

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