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) every first element has a corresp..
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) every first element has a corresp..Many-one function
Every one element of A corresponds to more than one element of B. In example 3, one image has three pre-images. In example 4, one image has four pre-images. Therefore, many-one relations in examples 3 and 4 are many-one functions. Consider the following examples and note why these relations are NO..
Every one element of A corresponds to more than one element of B. In example 3, one image has three pre-images. In example 4, one image has four pre-images. Therefore, many-one relations in examples 3 and 4 are many-one functions. Consider the following examples and note why these relations are NO..Range
The set of all the second elements of the ordered pairs of a function is called the rang..
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 fuction. In this chap..
Representation of a Function
A function can be represented by the following methods: (i) An arrow diagram. (ii) Cartesian graph. (iii) Set-builder notatio..
Test for Functions (Summary)
The relation should be one-one or many-one, and Every first element is mapped which means that every pre-image should have an imag..
Summary
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...
Following are the types of Functions:
(1) One-one function (2) Many-one function (3) Onto function (4) Into function Let the relation be from set A to set ..
2. Many-one function
There is many-one correspondence between the elements of the set A and the set B..
There is many-one correspondence between the elements of the set A and the set B..4. Into function
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 ONTO and INTO functions because e..
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 ONTO and INTO functions because e..See what our Users say :
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