Mathematics · Class 11
Relations and Functions
Learn Relations and Functions with notes, examples, and practice questions.
3 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Relations pair elements from two sets; functions are relations where each input has exactly one output. Class 11 focuses on domain, codomain, range, and types of real functions.
Relations
- Cartesian product A×B
- Relation R ⊆ A×B
- Domain, range of relation
- Equivalence relations (reflexive, symmetric, transitive)
Functions
Domain
All valid inputs x
Range
All output values f(x)
One-one
f(x₁)=f(x₂) ⇒ x₁=x₂
Onto
Range = codomain
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Domain of √(x−2)
Find domain.
- 1x−2 ≥ 0
- 2x ≥ 2
Answer
[2, ∞)
Range of x²
f(x)=x², codomain ℝ.
- 1x² ≥ 0 for all x
Answer
[0, ∞)
Key Points to Remember
- ✓ Vertical line test for functions
- ✓ Modulus, greatest integer, signum functions
- ✓ Polynomial, rational, trigonometric types
Exam Tips
- • State domain before range
- • Check denominator ≠ 0 for rational functions
Practice MCQs — Relations and Functions
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
Function assigns each input: