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Relations and Functions

Assam Board · Class 12 · Mathematics

Complete topic list for Relations and Functions in Assam Board Class 12 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

119 questions52 flashcards5 concepts

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4 Topics · Assam Board Class 12 Mathematics

Topics in Relations and Functions

1

1. Relations and Their Types

  • A relation in a set A is a subset of A × A.
  • The two extreme relations are the empty relation ϕ and the universal relation A × A.
  • Empty relation means no element of A is related to any element of A.
2

2. Functions: One-One, Onto, and Bijective

  • A function is a special relation with a well-defined image for each element of the domain.
  • One-one means distinct elements of the domain have distinct images.
  • Many-one means at least two different domain elements have the same image.
3

3. Composition of Functions and Inverse

  • Composition means applying one function after another.
  • The notation gof means g(f(x)).
  • Composition is generally not commutative: gof may differ from fog.
4

4. Historical Development of Function

  • Descartes first used the word function in 1637 in Geometrie to mean a positive integral power x^n of a variable x.
  • James Gregory considered a function as a quantity obtained from other quantities by algebraic or other operations.
  • Leibnitz used the word function for quantities varying along a curve and was the first to use the phrase function of x.

Key Concepts

Central concept: Relations and Functions

RelationsTypes of relationsEquivalence classesFunctionsExamples of functionsComposition of functionsInvertible functionsSpecial results on finite and infinite sets

Frequently Asked Questions

What are the important topics in Relations and Functions for Assam Board Class 12 Mathematics?
Relations and Functions covers several key topics that are frequently asked in Assam Board Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Relations and Functions — Assam Board Class 12 Mathematics?
Understand the core concepts first, then work through the 119 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All 15 chapters — Assam Board Class 12 Mathematics Syllabus

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