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Relations and Functions

Relations & Functions-Types of Functions: Classification, One-One, Onto, Examples-Class 12 Math Chapter 1 Notes Download free pdf

August 22, 2025January 6, 2025 by Neeraj Anand, Param Anand
Functions are defined as the relations which give a particular output for a particular input value. A function has a domain and codomain (range). F(x) usually denotes a function where x is the input of the function. In general, a function is written as y = f(x).

Functions are defined as the relations which give a particular output for a particular input value. A function has a …

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Composite functions-Relations & functions Class 12 Math Chapter 1 Notes Study Material Download free pdf

January 6, 2025 by Neeraj Anand, Param Anand
Let f : a->b and g : b->c be two functions. Then the composition of f and g, denoted by g o f, is defined as the function g o f : a->c given by g o f (x) = g{f(x)}, ∀ x ∈ a.

Composite Functions Let f : A->B and g : B->C be two functions. Then the composition of f and g, …

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Invertible Functions-Graph, Solved Examples & FAQs, Relations & functions Class 12 Math Chapter1 Notes Study Material Download free pdf

January 6, 2025 by Neeraj Anand, Param Anand
As the name suggests invertible means “inverse“, and invertible function means the inverse of the function. Invertible functions, in the most general sense, are functions that “reverse” each other. For example, if f takes a to b, then the inverse, f-1, must take b to a.

As the name suggests Invertible means “inverse“, and Invertible function means the inverse of the function. Invertible functions, in the …

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Composition of Functions: Definition, Domain, Range, Examples, Relations & functions Class 12 Math Chapter 1 Notes Study Material Download free pdf

January 6, 2025 by Neeraj Anand, Param Anand
Composition of function is the process or operation which combines two or more functions together into a single function. We define functions as the set of operations that operate on a set of values and give the desired output. Suppose f is a function say a function which draws the sketch of the fruits whose name we enter, here, the name given by us is the input value and the sketch of the fruit is the output value. Similarly, imagine any other function g which colors the given sketch.  

Composition of Function is the process or operation which combines two or more functions together into a single function. We …

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Inverse Functions, Graphs & Solved Examples, Relations & functions Class 12 Math Chapter 1 Notes Study Material Download free pdf

January 6, 2025 by Neeraj Anand, Param Anand
Inverse functions are an important concept in mathematics. An inverse function basically reverses the effect of the original function. If you apply a function to a number and then apply its inverse, you get back the original number. For example, if a function turns 2 into 5, the inverse function will turn 5 back into 2.

Inverse Functions are an important concept in mathematics. An inverse function basically reverses the effect of the original function. If you …

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Relations & Functions Exercise 2.1 NCERT Solutions for Class 11 Maths Chapter 2 Free PDF Download

January 7, 2025 by Neeraj Anand, Param Anand
This section provides detailed solutions for exercise 2. 1 from chapter 2 of the class 11 ncert mathematics textbook. The exercise includes problems in identifying and representing relations and functions, determining the domain and range, and working with function notation. The solutions are presented step-by-step to help students understand the methods for solving these problems and applying the concepts of relations and functions effectively.

NCERT Solutions for Class 11 – Chapter 2 Relations and Functions – Exercise 2.1 This section provides detailed solutions for …

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Relations & Functions Exercise 2.2 NCERT Solutions for Class 11 Maths Chapter 2 Free PDF Download

January 7, 2025 by Neeraj Anand, Param Anand
This section provides detailed solutions to the problems in exercise 2. 2 of chapter 2, “relations and functions,” from the class 11 ncert mathematics textbook. The exercise focuses on different types of functions, including one-to-one, onto, and bijective functions, as well as the methods to determine and prove these properties.

NCERT Solutions for Class 11 – Mathematics – Chapter 2 Relations and Functions – Exercise 2.2 This section provides detailed …

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Relations & Functions Exercise 2.3 NCERT Solutions for Class 11 Maths Chapter 2 Free PDF Download

January 7, 2025 by Neeraj Anand, Param Anand
Exercise 2. 3 deals with analyzing different types of functions and their properties. Key aspects include:

NCERT Solutions for Class 11 – Mathematics – Chapter 2 Relations and Functions – Exercise 2.3 Exercise 2.3 deals with …

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Relations & Functions Miscellaneous Exercise NCERT Solutions for Class 11 Maths Chapter 2 Free PDF Download

January 7, 2025 by Neeraj Anand, Param Anand
In this article, we will be going to solve the entire miscellaneous exercise of chapter 2 of the ncert textbook. Relations and functions are fundamental concepts in mathematics, particularly in algebra and calculus. They describe how elements from one set can be associated with elements from another set.

In this article, we will be going to solve the entire Miscellaneous Exercise of Chapter 2 of the NCERT textbook. …

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Relations & Functions Exercise 1.1 NCERT Solutions Class 12 Math Chapter 1 free PDF Download

January 7, 2025 by Neeraj Anand, Param Anand
Relation and function are two ways of establishing links between two sets in mathematics. Relation and function in maths are analogous to the relation that we see in our daily lives i. E. , two persons are related by the relation of father-son, mother-daughter, brother-sister, and many more. On a similar pattern, two numbers can be related to each other as one number is the square of another number and many more. A function is a special kind of relation that is defined as a unique relation between two mathematical entities.

Relation and Function are two ways of establishing links between two sets in mathematics. Relation and Function in maths are …

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Relations & Functions Exercise 1.2 NCERT Solutions Class 12 Math Chapter 1 free PDF Download

January 7, 2025 by Neeraj Anand, Param Anand
In class 12 mathematics, chapter 1, “relations and functions” students delve into the foundational concepts of relations and functions. Exercise 1. 2 focuses on the various problems to enhance understanding of these concepts. This exercise is crucial for grasping how different functions relate to each other and how they can be represented mathematically.

In Class 12 Mathematics, Chapter 1, “Relations and Functions” students delve into the foundational concepts of relations and functions. Exercise …

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Relations & Functions Exercise 1.3 NCERT Solutions Class 12 Math Chapter 1 free PDF Download

January 7, 2025 by Neeraj Anand, Param Anand
Exercise 1. 3 delves into the advanced concepts of function composition and invertible functions, building upon the foundational knowledge of relations and functions established earlier in the chapter. This exercise is crucial for developing a deeper understanding of how functions interact and transform, paving the way for more complex mathematical analysis. Students will explore the process of combining functions through composition, understand the conditions under which functions can be inverted, and learn to find and work with inverse functions. These skills are fundamental in various branches of mathematics, including calculus, abstract algebra, and complex analysis, and have wide-ranging applications in fields such as physics, engineering, and computer science. Mastering the concepts in this exercise will equip students with powerful tools for solving sophisticated problems and understanding the intricate relationships between mathematical entities.

Exercise 1.3 delves into the advanced concepts of function composition and invertible functions, building upon the foundational knowledge of relations …

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Relations & Functions Miscellaneous Exercise NCERT Solutions Class 12 Math Chapter 1 free PDF Download

January 7, 2025 by Neeraj Anand, Param Anand
Solution:

Class 12 NCERT Solutions- Mathematics Chapter 1 Relations And Functions -Miscellaneous Exercise on Chapter 1 Question 1. Let f : R …

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