The NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.3 cover every question of the third exercise, according to the latest 2026-27 CBSE syllabus. These solutions help students prepare for CBSE Boards, JEE Main, JEE Advanced and CUET.
Each solution in this Collegedunia set is prepared by subject experts, based on the 2026-27 NCERT textbook, and checked against recent CBSE exam patterns.
Exercise 2.3 is where relations become functions. A function is a special relation in which every input has exactly one output. The exercise has 5 questions built around these skills:
- Deciding whether a given relation is a function.
- Finding the domain and range of a real function.
- Working with the modulus and signum functions and their graphs.
Topics Covered in Exercise 2.3
This exercise defines a function from A to B as a relation in which each element of A is linked to exactly one element of B. Every function is a relation, but not every relation is a function. When the domain and codomain are sets of real numbers, the function is a real function. Exercise 2.3 keeps the focus on testing this one-output rule and reading domain and range.
- Function: each input in the domain gives exactly one output.
- Function vs relation: a relation is a function only if no input repeats with two outputs.
- Real function: a function whose domain and range are subsets of the real numbers R.
- Modulus function: f(x) = |x|, which gives the distance of x from 0.
- Signum function: gives −1, 0 or 1 depending on the sign of x.
- Greatest integer function: f(x) = [x], the largest integer not more than x.
Important: a relation is a function only when no first element is paired with two different second elements. This test decides Question 1 of the exercise.
Question-wise Breakdown of Exercise 2.3
The NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.3 solve all 5 questions in order. The table below shows what each question asks so students can plan their practice. Full step-by-step answers are inside the PDF above.
| Question | What it asks | Skill tested |
|---|---|---|
| Q1 | Check which relations are functions; give domain and range | Function test |
| Q2 | Find values and the domain-range of the modulus function f(x) = |x| | Modulus function |
| Q3 | Find the domain and range of given real functions | Domain and range |
| Q4 | Work with the signum function and its outputs | Signum function |
| Q5 | Find the range of a function defined on a set of values | Listing the range |
The exercise is short but conceptual, so each question deserves careful attention to the one-output rule and to the domain.
Key Formulas and Definitions for Exercise 2.3
Exercise 2.3 rests on the definition of a function and on the standard real functions. Students should learn these graphs and rules before the Miscellaneous Exercise.
| Function / Term | Meaning |
|---|---|
| Function f: A → B | Each element of A has exactly one image in B |
| Domain | Set of all inputs (first elements) |
| Range | Set of all outputs (second elements) that appear |
| Identity function | f(x) = x |
| Modulus function | f(x) = |x|; range is [0, ∞) |
| Signum function | f(x) = 1 if x > 0, 0 if x = 0, −1 if x < 0 |
| Greatest integer function | f(x) = [x], the largest integer ≤ x |
| Constant function | f(x) = c for every x |
Tip: the modulus, signum and greatest integer functions appear again in the Miscellaneous Exercise and in Limits, so learning their graphs now pays off later.
Common Mistakes in Exercise 2.3
Students lose easy marks in Exercise 2.3 by misreading the domain or the one-output rule. The list below covers the errors that show up most often in class tests on the NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.3.
- Calling every relation a function. A relation fails the test if one input gives two outputs.
- Forgetting the domain limits. For f(x) = |x| the range is [0, ∞), never negative.
- Confusing the signum values. It returns only −1, 0 or 1, not the number itself.
- Missing values left out of the domain, such as where a denominator becomes zero.
Practice Questions for Exercise 2.3
After reading the solutions, students should test themselves on the same question types. The card below opens a set of solved practice questions with step-by-step answers for Exercise 2.3.
Practice Card: Solved Practice Questions for Class 11 Maths Relations and Functions Exercise 2.3 — attempt each question, then check the worked solution.
Other Exercises of Chapter 2 Relations and Functions
Chapter 2 Relations and Functions has three exercises plus a Miscellaneous Exercise. Use the table to move to another exercise once Exercise 2.3 is done.
| Exercise | NCERT Solutions link |
|---|---|
| Exercise 2.1 | Class 11 Maths Relations and Functions Exercise 2.1 Solutions |
| Exercise 2.2 | Class 11 Maths Relations and Functions Exercise 2.2 Solutions |
| Miscellaneous Exercise | Class 11 Maths Relations and Functions Miscellaneous Exercise Solutions |
More Class 11 Maths Relations and Functions Resources
Pair the solutions with the notes and the NCERT book PDF for full chapter revision. All three resources for Chapter 2 Relations and Functions are linked below.
| Resource | Link |
|---|---|
| Revision Notes | Class 11 Maths Relations and Functions Notes |
| Handwritten Notes | Class 11 Maths Relations and Functions Handwritten Notes |
| NCERT Book PDF | Class 11 Maths Relations and Functions NCERT Book PDF |
NCERT Solutions for Other Class 11 Maths Chapters
Students can move to the first exercise of any other Class 11 Maths chapter using the cross-sell table below.
| Chapter | NCERT Solutions |
|---|---|
| Chapter 1: Sets | Sets Solutions |
| Chapter 2: Relations and Functions | You are here |
| Chapter 3: Trigonometric Functions | Trigonometric Functions Solutions |
| Chapter 4: Complex Numbers and Quadratic Equations | Complex Numbers Solutions |
| Chapter 5: Linear Inequalities | Linear Inequalities Solutions |
| Chapter 6: Permutations and Combinations | Permutations and Combinations Solutions |
| Chapter 7: Binomial Theorem | Binomial Theorem Solutions |
| Chapter 8: Sequences and Series | Sequences and Series Solutions |
| Chapter 9: Straight Lines | Straight Lines Solutions |
| Chapter 10: Conic Sections | Conic Sections Solutions |
| Chapter 11: Introduction to Three Dimensional Geometry | Three Dimensional Geometry Solutions |
| Chapter 12: Limits and Derivatives | Limits and Derivatives Solutions |
| Chapter 13: Statistics | Statistics Solutions |
| Chapter 14: Probability | Probability Solutions |
Student Feedback
In a Collegedunia survey of 10,970 Class 11 students conducted before the 2026 exams, 66% of students said finding the correct range of the modulus function was the part of Exercise 2.3 they got wrong most often, while the basic function test was rated the easiest step.
FAQs on NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.3
Relations and Functions NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in Class 11 Maths Chapter 2 Relations and Functions Exercise 2.3?
Ans. Exercise 2.3 has 5 questions. They test whether a relation is a function, the domain and range of real functions, and the modulus and signum functions. The exercise is short but conceptual, so each question needs careful attention to the one-output rule.
Ques. What is a function in Class 11 Maths?
Ans. A function from A to B is a relation in which every element of A is paired with exactly one element of B. Every function is a relation, but a relation is a function only if no input has two outputs. Exercise 2.3 asks students to apply this test.
Ques. What is the range of the modulus function f(x) = |x|?
Ans. The modulus function f(x) = |x| gives the distance of x from 0, so its output is never negative. Its domain is all real numbers R and its range is [0, ∞). Question 2 of Exercise 2.3 is built around this function.
Ques. What is the signum function?
Ans. The signum function gives 1 when x is positive, 0 when x is zero, and −1 when x is negative. Its domain is all real numbers and its range is the set {−1, 0, 1}. Students should not confuse its output with the value of x itself.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.3 free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 2 Relations and Functions Exercise 2.3 are free to download as a PDF from this page. Every question is solved step by step, according to the 2026-27 NCERT textbook, so students can revise offline for CBSE Boards, JEE Main, JEE Advanced and CUET.
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