← CBSE Class 11
Relations and Functions
Chapter Overview
The Cartesian product of two sets A and B, denoted A x B, is the set of all ordered pairs (a, b) where a in A and b in B. A relation R from A to B is a subset of A x B. Functions are special relations where each element of the domain relates to exactly one element of the codomain.
Key types include one-to-one, onto, and bijective functions. The chapter covers domain, codomain, range, algebra of functions, and composition. Real-valued functions include polynomial, rational, modulus, signum, and greatest integer functions.
Topics Covered
- Ordered Pairs and Cartesian Product
- Relations and Types
- Domain and Range
- Functions Definition
- One-to-One and Onto
- Algebra of Functions
- Composition of Functions
- Modulus and Signum Functions
Key Formulas
n(A x B) = n(A) x n(B)
(f + g)(x) = f(x) + g(x)
(f o g)(x) = f(g(x))
Real-World Applications
Applications: Functions model relationships in physics, economics, engineering, and computer science.
Study Tips
Tip: Practice domain-finding for all function types
Tip: Draw graphs to understand function behavior
Tip: Master composition of functions