Class 11 Maths - ISC

Relations and Functions

The chapter 'Relations and Functions' in Class 11 ISC Mathematics builds the foundation for advanced calculus and algebra by introducing ordered pairs, Cartesian products of sets, and the formal definition of relations and functions. Students learn to determine domains, co-domains, and ranges, alongside graphing various standard functions like modulus, greatest integer, and polynomial functions. Mastery of this chapter is crucial for board exams as it carries substantial weightage and forms the base for calculus, limits, and inverse trigonometric functions in Class 12.

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Key Concepts

Cartesian Product

The set of all ordered pairs (a, b) such that a belongs to set A and b belongs to set B, denoted as A × B.

Relation

A subset of the Cartesian product A × B, establishing a connection between the first element and the second element based on a given condition.

Function

A special type of relation where every element in the domain has a unique and distinct image in the co-domain.

Domain and Range

The domain is the set of all possible input values for a relation or function, while the range is the set of all resulting output values.

Algebra of Real Functions

Rules for combining functions through addition, subtraction, multiplication, and division, valid wherever both component functions are defined.

Important Formulas

n(A × B) = n(A) × n(B)

Total number of relations from set A to set B = 2^(n(A) × n(B))

(f + g)(x) = f(x) + g(x)

(f - g)(x) = f(x) - g(x)

(f · g)(x) = f(x) · g(x)

(f / g)(x) = f(x) / g(x), provided g(x) ≠ 0

Board Exam Info

In the ISC Class 11 Mathematics examination, this chapter typically carries around 6 to 8 marks. Questions frequently appear as short-answer problems finding the domain and range of given functions, or long-answer questions proving whether a relation is reflexive, symmetric, or transitive, and determining the inverse of bijective functions.

Frequently Asked Questions

What is the difference between a relation and a function?

How do I find the domain and range of a rational function?

Are all types of functions tested in the ISC Class 11 exam?

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More Maths Chapters - ISC Class 11

Sets Trigonometric Functions Complex Numbers And Quadratic Equations Linear Inequalities Permutations And Combinations Binomial Theorem Sequences And Series Straight Lines Conic Sections Introduction To Three Dimensional Geometry Limits And Derivatives Statistics Probability