Class 12 Maths Chapter 1 Relations and Functions Revision Notes
From assigning students to roll numbers and mapping cities to their pin codes to defining mathematical models used in engineering and computer science, Relations and Functions help establish meaningful connections between different quantities. This chapter extends the concepts learned in Class 11 by introducing types of relations, equivalence relations, composite functions, inverse functions, and binary operations. These concepts serve as the building blocks for advanced topics such as Calculus, Matrices, Vector Algebra, and Linear Transformations, making this chapter highly important for JEE Main, JEE Advanced, and CBSE Board examinations.
At ALLEN, our expert faculty have prepared these Class 12 Maths Chapter 1: Relations and Functions Revision Notes to help students revise the chapter efficiently with complete conceptual clarity. These notes include concise theory, important definitions, standard formulas, shortcut techniques, solved illustrations, common exam traps, and PYQ-based insights. Whether you're preparing for CBSE Board exams or competitive exams like JEE Main and JEE Advanced, these revision notes will help you strengthen your fundamentals and solve questions with confidence.
1.0Chapter Snapshot
2.0Related Supporting Resources
3.0Learning Outcomes
After completing these revision notes, you will be able to:
- Differentiate between various types of relations.
- Identify reflexive, symmetric, transitive, and equivalence relations.
- Classify functions as one-one, onto, and bijective.
- Evaluate composite functions and determine inverse functions.
- Solve problems involving binary operations.
- Understand the algebra of functions and identity functions.
- Apply concepts of relations and functions to JEE Main, JEE Advanced, and CBSE Board-level questions.
- Build a strong foundation for higher Mathematics and Calculus.
4.05-Minute Quick Revision
Must-Revise Concepts
- Relation
- Function
- Reflexive Relation
- Symmetric Relation
- Transitive Relation
- Equivalence Relation
- One-One Function
- Onto Function
- Bijective Function
- Composite Function
- Inverse Function
- Binary Operation
Important Formula Recall
- Composite Function: (f∘g)(x)=f(g(x))
- Identity Function: IA(x)=x
- Inverse Function f−1(f(x))=xf(f−1(x))=x
- Condition for Invertibility: A function must be both one-one and onto (bijective) to possess an inverse.
Important Properties
- Every equivalence relation is reflexive, symmetric, and transitive.
- Every inverse function exists only for a bijective function.
- Composition of functions is generally not commutative.
- Identity function acts as the neutral element under composition.
- Binary operations must satisfy the closure property on the given set.
5.0High Weightage Topics
6.0Formula Handbook
The following formulas and standard results are essential for solving questions from Relations and Functions in JEE Main, JEE Advanced, and CBSE examinations.
7.0Common Mistakes & JEE Tips
Relations and Functions is a concept-driven chapter. Most mistakes occur due to confusion between different types of relations and functions or incorrect verification of conditions.
8.0ALLEN Faculty Tips
- Master the definitions before attempting numerical problems.
- Draw mapping diagrams to visualize different types of functions.
- Learn standard examples of one-one, onto, bijective, and many-one functions.
- Verify all three conditions while checking equivalence relations.
- Practice inverse function questions from both algebraic and graphical perspectives.
- Revise important properties of binary operations regularly.
- Solve Previous Years' Questions (PYQs) to identify common question patterns.
9.0PYQ Trend Analysis
Relations and Functions is a foundational chapter for JEE Main and JEE Advanced. Questions are frequently asked on inverse functions, composite functions, one-one and onto mappings, and equivalence relations.
Note: The trend below is based on the analysis of previous years' JEE Main and JEE Advanced question papers. The exact number of questions may vary each year.
10.0Most Common Question Types
- Identifying reflexive, symmetric, transitive, and equivalence relations.
- Classifying functions as one-one, onto, bijective, or many-one.
- Finding the composition of two or more functions.
- Determining the inverse of a given function.
- Verifying whether an inverse exists.
- Solving problems involving binary operations.
- Finding the domain and range of composite functions.
- Mixed conceptual questions based on properties of relations and functions.
11.0Smart Revision Strategy
Follow this revision sequence for effective preparation:
- Revise the definitions of relations and different types of functions.
- Learn the properties of reflexive, symmetric, transitive, and equivalence relations.
- Practice identifying one-one, onto, and bijective functions.
- Solve questions on composite and inverse functions.
- Revise binary operations and their properties.
- Attempt mixed conceptual problems involving multiple function types.
- Practice Previous Years' Questions (PYQs).
- Finish with a timed chapter test to improve speed and accuracy.