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Learn Relations and Functions in Mathematics
Welcome to the critical foundational chapter of CBSE Class 12 Mathematics: Relations and Functions. Building upon the basic concepts of sets and mappings introduced in Class 11, this chapter takes a deeper dive into the specific mathematical linkages that bind different sets of data together. It serves as the absolute bedrock for understanding advanced calculus, including continuity, differentiability, and integration. In the real world, understanding how specific inputs map to specific outputs is essential for a wide variety of fields ranging from computer science and cryptography to economics and structural engineering. Mastering this chapter means unlocking the core logic that governs advanced mathematical modeling.
In this chapter, you will transition from simple set mappings to understanding the rigorous properties that define complex mathematical relationships. You will explore Types of Relations, focusing heavily on how to prove whether a relation is reflexive, symmetric, and transitive in order to classify it as an Equivalence Relation. Furthermore, the syllabus thoroughly covers Types of Functions, challenging you to prove whether a given function is One-One (Injective), Onto (Surjective), or Bijective. You will also learn to compute Composite Functions (such as f(g(x))) and logically determine the Inverse of a Function, mathematical skills that are crucial for algebraic manipulations.
The infographic above visually deconstructs the essential mapping rules for One-One (Injective) and Onto (Surjective) functions, illustrating how elements in domain X either map uniquely or comprehensively onto co-domain Y. In your CBSE Class 12 board exams, this chapter carries significant weight and is primarily tested through theoretical proofs—such as proving a given relation is an equivalence relation or demonstrating that a function is mathematically invertible. A quick, highly effective tip for scoring maximum marks in this section: always explicitly define the domain and co-domain of the function at the beginning of your answers, and practice writing step-by-step logical deductions for your equivalence proofs rather than just stating the final conclusion.
Grasping the abstract theoretical concepts of relations and functions can sometimes feel overwhelming, but you certainly don't have to tackle it alone. If you find equivalence relation proofs, bijective mapping, or calculating composite functions challenging, connect with highly experienced, verified CBSE Class 12 Mathematics tutors on the UrbanPro platform. Whether you prefer personalized one-on-one online sessions or focused offline tuition near you, UrbanPro offers a trusted directory of expert educators ready to simplify complex theories, provide targeted practice materials, and help you confidently achieve top board exam results.
Top Tutors who teach Relations and Functions
Top Tutor 
Mira Road East MIDC, Mira-Bhayandar 
20 yrs of Exp 
1 student 
73 hrs of classes completed 
500 per hour 
Online Classes 
Student's Home 
Tutor's home Rich experience of 34 years of teaching mathematics to 11th and 12th science and commerce classes. experience of tuting student aspiring for JEE, CET exams
Top Tutor Vesu, Surat 20 yrs of Exp 13 students 1241 hrs of classes completed 500 per hour Online Classes I have experience teaching Mathematics to Class 12 students, focusing on building strong conceptual understanding and problem-solving skills. I teach key topics such as Calculus (limits, derivatives, and integrals), Matrices, Determinants, Probability, and Vectors. My teaching approach includes explaining concepts step-by-step, solving examples on the board, and giving practice questions similar to board exam patterns. I regularly conduct revision tests, doubt-clearing sessions, and discuss previous years’ question papers to help students prepare effectively for board examinations. I encourage students to understand the logic behind formulas rather than memorizing them. My goal is to make mathematics easier, improve students’ confidence, and help them achieve good results in Class 12 board exams.
My Applied Maths teacher is highly knowledgeable and explains concepts with great clarity. They make even difficult topics easier to understand by breaking them down into simple steps and using practical examples. Their teaching style is patient and encouraging, which helps build confidence in solving problems. They are always willing to clear doubts and provide extra support when needed. Regular practice and structured lessons have improved my problem-solving skills significantly. Overall, their dedication and effective teaching methods make learning Applied Maths both enjoyable and productive, making them an excellent choice for tuition classes.
Top Tutor Pandav Nagar, Ghaziabad 9 yrs of Exp 10 students 22 hrs of classes completed 600 per hour Tutor's home I am an experienced, qualified teacher with over 9 years of experience in teaching Math across different boards including CBSE, ICSE and IGCSE and state board 9-12 and IIT JEE engineering entrance mathematics . I have worked in reputed institutes like Vibrant academy, Resonance in Kota and in Byjus and Modi School in Rajkot. Passionate about solving mathematical problems. And I have also been carrying out year of experience in Engineering Mathematics.
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Top Tutor Rajajinagar Mahaganapathi Nagar, Bangalore 15 yrs of Exp 52 students 4397 hrs of classes completed 400 per hour Online Classes Tutor's home I have done Post Graduation in Mathematics, Presidency college, Chennai University. I was a topper and a gold medalist in MSc Math Presidency College. I have been teaching math from last 15 years. I have taken tuitions for 12th Maths for students across different boards like CBSE, ICSE, IGCSE, ISC and State Board. I have an expertise in Math with an excellent track record. My focus is students' success. Conceptually , I make students strong so that they can handle any question in the exam. I give challenging problems in the class so that you can become competetive. Your future is very promising with me.
Mrs. Mala Ravishankar is an exceptional teacher. She understands the capability of the student and teaches accordingly. Because of her teaching experience, she knows and teaches the subject clearly and in a way that is easy to grasp. Overall, I am quite satisfied to have been taught by her.
Top Tutor Domlur, Bangalore 15 yrs of Exp 29 students 2720 hrs of classes completed 800 per hour Online Classes Taught college students for more than 15 years. I have taught several subjects. I also teach for competitive exams like NEET, PET, BITSAT, GATE ,CET. I also teach a variety of students starting from Class 10 to M.Tech for the engineering stream. I also prepare students for several competitive exams. I also guide them how to crack any exam.
Saurabh sir teaches Maths and Physics in a very clear and structured manner, making even difficult concepts easy to understand. His explanations are simple, practical, and focused, which helps in better exam preparation. He encourages us to ask questions and patiently clears every doubt. The classes are interactive and well-planned, helping improve both conceptual understanding and problem-solving skills
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FAQ
What is the chapter Relations and Functions about?
The chapter Relations and Functions provides a comprehensive overview of the core concepts related to Relations and Functions in Mathematics. It delves into the theoretical and practical aspects of the topic.
What are the key learning outcomes from this chapter?
Students will gain a deep understanding of the principles of Relations and Functions, learning to apply key concepts and solve related problems effectively.
Why is this chapter important for CBSE exams?
This chapter is a key part of the CBSE - Class 12 syllabus. Questions from Relations and Functions test a student's fundamental understanding and ability to apply concepts, making it crucial for scoring well.
How should students study this chapter using NCERT?
Students should read the NCERT theory thoroughly, focusing on definitions and diagrams. Solving the in-text questions and exercise problems is mandatory for a strong grip on the topic.
What common challenges do students face?
Students often find it challenging to master the specific terminologies and complex applications associated with Relations and Functions.
How does UrbanPro support chapter-wise preparation?
UrbanPro connects students with expert Mathematics tutors and provides curated resources like NCERT solutions and mock tests to help master Relations and Functions effectively.
Is this chapter essential for future studies?
Yes, the concepts learned in Relations and Functions are often prerequisites for advanced topics in higher grades, especially in competitive exams.
