Functions Definition: A relation ‘ f ’ from set X to set Y is a function if each element in set X is mapped to exactly one element in set Y 1. 2. 3. 4..4.5.6.7.8.

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Presentation transcript:

Functions Definition: A relation ‘ f ’ from set X to set Y is a function if each element in set X is mapped to exactly one element in set Y X Y f

Notation: The above function is written as f : X  Y

Verify whether following relations are functions or not. a. b. c. d. e.. g.h. k. l.m. n f X Y

Verify whether following relations are functions or not. a. b. c. d. e.. g.h. k. l.m. n f XY

Verify whether following relations are functions or not. a. b. c. d. e.. g.h. k. l.m. n f X Y

Verify whether following relations are functions or not. a. b. c. d. e.. g.h. k. l.m. n f X Y

Verify whether following relations are functions or not. a. b. c. d. e.. g f X Y

Terms related to functions: Domain Codomain image pre image range

In the given example the element 1is mapped to 5 and we can write it as 1  5. 5 is known as the image of 1 and 1 is the pre-image of 5. Consider the function f : X  Y The set X is the Domain of f. Domain of f is {1,2,3,4} The set Y is the Co-domain. Co-domain of f is {4,5,6,7,8} Ihe set of images is the range of f Range of f is { 4,5,6,8} X Y f

Types of function Into function one-one function ( 1-1 correspondence) on to function. ( Surjection)

In to function a. b. c. d. E.. g.h. k. l.m. n f

One to one function a. b. c. d. E.. g.h. k. l.m. n f

Onto function a. b. c. d. E.. g.h. k f