Mastering Relations and Functions: A Comprehensive Class 12 Maths Course by MathYug
In this course, you will learn about the fundamental concepts of relations and functions, including the different types of relations and functions, their properties, and their applications. The course will cover the following topics:
- Introduction to relations and functions: You will learn about the basic definitions and concepts of relations and functions, and how they are different from each other.
- Types of relations: You will learn about the different types of relations, including empty relations, universal relations, and equivalence relations. The properties of each type of relation will be discussed in detail.
- Properties of relations: You will learn about the different properties of relations, such as reflexive relations, symmetric relations, and transitive relations. The course will also cover how to identify relations with specific properties.
- Types of functions: You will learn about the different types of functions, including one-to-one functions, onto functions, and bijective functions. The properties of each type of function will be discussed in detail.
- Composition of functions: You will learn about how to compose functions and how to find the domain and range of composite functions.
- Inverse of a function: You will learn about how to find the inverse of a function and the properties of inverse functions.
Throughout the course, you will have access to high-quality video lectures, which will provide expert explanations of each topic. You will also have access to PDF notes and assignments, which will help you deepen your understanding of the concepts covered in the course. The assignments will feature carefully selected questions from a variety of authoritative sources, including NCERT Textbook exercises, NCERT Examples, Board’s Question Bank, RD Sharma, NCERT Exemplar, and more.
By the end of the course, you will have a comprehensive understanding of the concepts of relations and functions, including their properties and applications. You will be able to solve problems and answer questions related to relations and functions with confidence.
MathYug have created a series of sample videos for Relations and Functions in Class 12 Maths that are designed to help students better understand this important topic.
These videos cover a wide range of concepts related to relations and functions, including domain and range, types of relations, composition of functions, inverse functions, and more. They use a combination of clear explanations, examples, and practice problems to help students develop a deep understanding of the material.
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Whether you are a student who is struggling with this topic or just looking to improve your skills, MathYug’s sample videos for Relations and Functions in Class 12 Maths can help you succeed.
Lecture — 6 | Equivalence Relation and Equivalence Class | Class 12 Maths | MathYug
In this video, we explore the concept of equivalence relation and equivalence class, using the example of a relation defined over the set A = {1, 2, 3, … , 12}. Through a step-by-step proof, we demonstrate how this relation satisfies the three properties of an equivalence relation, namely, reflexivity, symmetry, and transitivity. We also obtain the equivalence class [(3, 4)] and discuss its properties.
Question 12: Let A = {1, 2, 3, … , 12} and R be a relation in A times A defined by (p, q) R (r, s) if ps = qr for all (p, q), (r, s) in A times A . Prove that R is an equivalence relation. Also obtain the equivalence class [(3, 4)].
Lecture — 9 | Inverse of functions | Invertible Functions | Relations and Functions Class 12 Maths
In this video from MathYug, we cover the topic invertible functions of chapter 1, “Relations and Functions” from Class 12 Maths. We explain the concepts in a clear and easy-to-understand manner, with examples and diagrams to illustrate key points. Questions discussed in this video:
Question 3. Let f : X to Y be an invertible function. Show that f has unique inverse. (N)
Question 8. Let f:R-{4/3} to R be a function defined as f(x)=4x/(3x+4). The inverse of f is the map g:Range of f to R — 4/3 given by a. g(y)=3y/(3–4y) b. g(y)=4y/(4–3y) c. g(y)=4y/(3–4y) d. g(y)=3y/(4–3y)
Question 1. Consider f:R_+ to [4, infinity ) given by f(x) = x² + 4. Show that f is invertible with the inverse f^{-1} of f given by f^{-1}(y)=sqrt{y-4}, where R_+ is the set of all non-negative real numbers.
Question 2. Consider f : R_+ to [-5, infinity ) given by f(x) = 9x² + 6x — 5. Show that f is invertible with f^{-1}(y) = ( sqrt{y+6}-1/3 ).
Question 3. Let f’ : N to R be a function defined as f’(x) = 4x² + 12x + 15. Show that f:N to S, where, S is the range of f, is invertible. Find the inverse of f.
If you want to learn more, the full video course on this chapter is available on our website:
The course includes 8 hours and 22 minutes of video content, spread across 10 lectures, to help you master this topic and ace your exams. Check it out now and start learning with MathYug!
