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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 chapter, we will study how a function is a relation, but a relation may not be a function.
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Function |
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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. |
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Representation of a Function |
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A function can be represented by the following methods:
(i) An arrow diagram. (ii) Cartesian graph. (iii) Set-builder notation. |
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Types of Functions (Mapping) |
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The following are the Types of Functions or Mapping:
(1) One-one function
(2) Many-one function
(3) Onto function
(4) Into function. |
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Test for Functions (Summary) |
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The relation should be one-one or many-one, and
Every first element is mapped which means that every pre-image should have an image. |
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More Solved Examples |
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The mathematical concept of a function expresses the intuitive idea of deterministic dependence between two quantities, one of which is viewed as primary (the independent variable, argument of the function, or its "input") and the other as secondary (the value of the function, or "output"). |
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Summary |
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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.
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