Relations and Functions

Relations

An ordered pair consists of two objects or elements in a fixed order. It is written in the form (a, b) where, a is called the ‘first component’ and b is called the ‘second component’.
The cartesian product of two non-empty sets A and B is defined as the set of all ordered pairs (a, b) whe
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Basics of Function

A relation f from a set A to set B is said to be a function if every element of set A has one and only one image in set B.
Vertical line test is used to determine if a relation is a function or not. A relation is a function if vertical lines intersect the graph only at one point.
Let A and B b
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Graphs of Functions

A relation f from a set A to set B is said to be a function if every element of set A has one and only one image in set B.
Vertical line test is used to determine if a relation is a function or not. A relation is a function if vertical lines intersect the graph only at one point.
Let A and B b
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Algebra of Functions

A set of all rational and irrational numbers is called real numbers, and it is denoted by R.

A relation f from a non-empty set A to a non-empty set B is said to be a function, if:
(i) an element of set A is associated to a unique element in set B.
(ii) all the elements of set A are as
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