What is Function

Duration: 6 min

This video lesson is available to enrolled students.

Return to /learn/UP-LT-GRADE-ASSISTANT-TEACHER-2025/digital-logic-circuits-discrete-math-structures/functions/definition-of-a-function-domain-co-domain-range-and-count-of-possible-functions/asset-what-is-function after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. CS | 01 | Digital Logic and Circuits and Discrete Mathematical Structures: Digital Systems & Boolean Basics, Number System, Number Representation, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Permutation and Combination
  3. CS | 02 | Computer Organization and Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Multiprocessors
  4. CS | 03 | Data Structures and Algorithm: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Complexity Theory, Advanced Algorithms
  5. CS | 04 | Problem Solving through C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  6. CS | 05 | Object Oriented Techniques: Object Oriented Technology, Java
  7. CS | 06 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Unix OS
  8. CS | 07 | Database Management Systems: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, Database Security & Authorization, Query Processing & Optimization, File Organization & Indexing
  9. CS | 08 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics
  10. CS | 09 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  11. CS | 10 | Internet Technology, Web Design and Web Technology: Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, JavaScript-Basics, HTML Basics
  12. CS | 11 | System Analysis And Design: Fundamentals of Systems and Information Systems, SDLC and Development Approaches, Software Documentation and Software Requirements Specification (SRS), SDD and Quality Assurance, Security, Risk Management & Maintenance
  13. CS | 12 | Information Security and Cyber Laws: Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Electronic Data Interchange and E-Commerce, Physical Security and Cryptography Basics, Intrusion Detection Systems (IDS), Cyber Safety and Security
  14. CS | 13 | Computer Graphics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing
  15. GS Paper | 01 | Indian and World Geography: Geography
  16. GS Paper | 02 | History: History
  17. GS Paper | 03 | Indian Economy & Social Development: Indian Economy
  18. GS Paper | 04 | General Science: Biology, Chemistry, वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research
  19. GS Paper | 05 | Elementary Maths: संख्या पद्धति / Number System, Divisibility Rules, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, प्रतिशत / Percentage, लाभ, हानि और बट्टा / Profit, Loss and Discount, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, अनुपात और समानुपात / Ratio and Proportion, औसत / Average, समय और कार्य / Time and Work, समय, चाल और दूरी / Time, Speed and Distance, Algebra, घन क्षेत्रमिति / Solid Mensuration, आँकड़ा निर्वचन / Data Interpretation, Arithmetic, Statistics, Probability, Sequence and Series (Series), मिश्रण और एलिगेशन / Mixture and Alligation, Calculus, Trigonometry, Vectors, संख्या पद्धति और संख्या सिद्धांत / Number Systems and Number Theory, यूक्लिडीय ज्यामिति और क्षेत्रमिति / Euclidean Geometry and Mensuration, सांख्यिकी और प्रायिकता / Statistics and Probability, निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति / Coordinate Geometry, Vectors and 3D Geometry, बहुपद, समीकरण और सम्मिश्र संख्याएँ / Polynomials, Equations and Complex Numbers, समतल क्षेत्रमिति / Plane Mensuration, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics
  20. GS Paper | 06 | Indian Polity and Governance: Polity
  21. GS Paper | 07 | Current Events: समसामयिकी / Current Affairs
  22. UPLT Live Classes Notes: UPLT Live Classes
  23. UPLT Full Mock Tests Tier 1:
  24. UPLT Full Mock Tests Tier 2:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a foundational lecture on the mathematical concept of a function. The instructor begins by contextualizing functions as central objects in mathematics. He uses a specific counter-example involving sets X = {1, 2, 3, 4, 5} and Y = {2, 3, 4, 5, 6, 7} to demonstrate why a relation might not be a function. The lecture transitions to a formal definition, explaining that a function must associate every element of a first set with exactly one element of a second set. Key terminology including Domain, Co-Domain, and Range are introduced using set notation and diagrams. The instructor clarifies that the Range is a subset of the Co-Domain.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor begins by stating functions are central to mathematics. He presents a specific example with sets X = {1, 2, 3, 4, 5} and Y = {2, 3, 4, 5, 6, 7}. He displays a diagram where a relation R exists between these sets. He explains this is a valid relation but fails to be a function for two reasons: first, element 3 in set X has no outgoing arrow, meaning it is not participating. Second, element 5 in set X has multiple arrows pointing to 4, 5, and 7 in set Y, violating the "one output" rule. He writes the mathematical hierarchy X * Y >= R >= F on the screen to illustrate that the Cartesian product contains all relations. He circles element 5 to highlight the "one-to-many" violation.

  2. 2:00 – 5:00 02:00-05:00

    The lecture transitions to a formal definition slide. The text states a function associates "every element of a first set exactly one element of the second set." The notation f: A -> B is introduced. A new diagram shows Set X with elements {a, b, c} mapping to Set Y with elements {1, 2, 3}. Here, all elements in X map to 1. The instructor annotates the diagram, labeling Set X as the "Domain" and Set Y as the "Co-Domain". He circles element 1 in Set Y and labels it the "Range". He writes the set-builder notation for Range: {y | y in B and (x, y) in f}. He emphasizes that the Range is a subset of the Co-Domain (Range <= B).

  3. 5:00 – 5:40 05:00-05:40

    The instructor continues to elaborate on the definitions provided in the previous segment. He reinforces the distinction between the Co-Domain (the entire target set Y) and the Range (the specific subset of Y that is actually mapped to). The slide remains visible with the diagram and formulas. The focus is on solidifying the student's understanding of the mapping properties required for a function, specifically the uniqueness of the image for every domain element.

The lesson follows a logical progression from intuition to formalism. It first establishes the necessary conditions for a function by showing violations in a general relation: unmapped elements and one-to-many mappings. This sets the stage for the formal definition where "every element" must map to "exactly one element." The instructor visually distinguishes the Domain (input set) from the Co-Domain (potential output set) and defines the Range as the actual output set. The notation f: A -> B and the set-builder formula for Range are provided for precise mathematical communication. The hierarchy X * Y >= R >= F is used to show that functions are a specific, restricted type of relation.

Loading lesson…