Relations and Functions
Karnataka Board · Class 11 · Mathematics
Quick revision notes for Relations and Functions — Karnataka Board Class 11 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Cartesian Products of Sets
- Ordered pairs maintain specific sequence: (a,b) ≠ (b,a) unless a = b
- Cartesian product A × B contains all possible ordered pairs from sets A and B
- Number of elements in A × B equals n(A) × n(B)
Relations
- Relations are subsets of Cartesian products with specific conditions
- Domain consists of all first elements in the relation
- Range consists of all second elements (outputs) in the relation
Functions
- Functions are special relations where each input has exactly one output
- Every element in domain must have an image in codomain
- No element in domain can have multiple images
Algebra of Real Functions
- Real functions can be added, subtracted, multiplied, and divided
- Operations are performed point-wise: (f+g)(x) = f(x) + g(x)
- Domain of combined functions is intersection of individual domains
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Relations and Functions covers several key topics that are frequently asked in Karnataka Board Class 11 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
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Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision before the exam.
Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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