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The MathYug course aims to equip you with the fundamental concepts of relations and functions, covering their different types, properties, and applications. Its purpose is to help you develop a deeper understanding of these concepts and prepare you for relevant exams.

The course features high-quality video lectures, PDF notes, and assignments created by experienced mathematics teachers. The assignments contain carefully chosen questions from various authoritative sources, such as NCERT Textbook exercises, NCERT Examples, Board's Question Bank, RD Sharma, and NCERT Exemplar, among others.

Upon completing the MathYug course, you will have a comprehensive understanding of relations and functions, their properties, and applications. You will be able to confidently solve problems and answer questions related to these concepts, which will significantly enhance your readiness for relevant exams.

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Class 11th/ 12th Tuition, Mathematics, CA/ CS Exam, Engineering Entrance/ IIT-JEE; Exp: More than 15 year

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) = x^2 + 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) = 9x^2 + 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) = 4x^2 + 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 at 
https://mathyug.com/class-12-maths/chapter-1/.
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!

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MathYug (Ashish Kumar - Let's Learn)

Lecture - 9 | Inverse of functions | Invertible Functions | Relations and Functions Class 12 Maths

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)].

To learn more about this topic and other important concepts in Class 12 Maths, check out our full course with over 6 hours of content and 8 lectures on our website at 

https://mathyug.com/class-12-maths/chapter-1/. 

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Website: https://mathyug.com

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