BoardStudy given class 11 math Relations and Functions notes according to latest NCERT syllabus to make your study more convenient and easy. We have covered every topic in a simple and easy way so anyone can understand the chapter and perform well in the exam.
Notes are very clean and colourful written by BoardStudy subject matter experts. Every important concept, formula, diagram and derivation is shared in the Relations and Functions notes that will help you solve the problem. By reviewing these notes regularly you will master the Relations and Functions chapter and can score well in exam.
Class 11 Math Relations and Functions Notes
Chapter 1: Sets Notes
Chapter 3: Trigonometric Functions Notes
Key Points Relations and Functions
Relations
A relation R from a non-empty set A to a non-empty set B is a subset of the cartesian product A × B.
The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.
Image
The second element of the ordered pairs in A × B is called image of first element.
Domain
The set of all first elements of the ordered pairs in a relation R from a set A to a set B is called domain of the relation R.
Range
The set of all second elements in a relation R from a set A to a set B is called the range of relation R.
Codomain
The whole set B is called codomain of the relation R.
Inverse of Relation
For any two non-empty sets A and B, let R be a relation from a set A to a set B. Then the inverse of relation R, denoted by R⁻¹, is a relation from B to A and it is defined by
R⁻¹ = { (b, a) : (a, b) ∈ R }
Domain of R = Range of R⁻¹
Range of R = Domain of R⁻¹
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.
If f is a function from A to B and (a, b) ∈ f then
f(a) = b, where
b is called the image of a under f.
a is called the preimage of b under f.
Real valued function
A function which has either R or one of its subsets as its range.
Real function
If A and B both are subsets of R, then f is called a real function.