What is Function

Duration: 6 min

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Inside: a video lesson and guided study material.

Module outline

  1. General Intelligence & Reasoning: Analogy, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Blood Relations, Directions (Direction Test), Ranking, Order and Sequence, Logical Sequence Of Words, Syllogisms, Venn Diagram, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Data Sufficiency, Puzzle Solving (Puzzles), Data Arrangement, Cubes & Dices, Calendar, Clock, Arithmetic, Number System, HCF LCM, Verbal Analogy (Word Based Analogy), Visual Recognition and Figure Completion, Paper Folding and Cutting, Transformation of Shapes, Clocks and Calendars, Direction Sense, Cubes and Dice, Patterns in Two-Dimensional Figures, Seating Arrangements, Analogy and Classification, Logical Deduction and Induction, Alphabet and Word Tests, Mathematical Operations, Series Completion, Simplification and Approximation, Coding and Decoding, Numerical Reasoning, Assembling and Grouping of Shapes, Three-Dimensional Patterns and Visualization, Vocabulary, Number System, Averages, Mixtures and Alligation, Simple and Compound Interest, Percentages, Algebra, Speed, Time and Distance, Seating and Arrangement Puzzles, Traverse Surveying, Order, Ranking and Sequence, Constraint Puzzles, Syllogisms and Venn Diagrams, Reading Comprehension, Critical Reasoning, Permutations and Combinations, Narrative Sequencing, Project Monitoring, Resources and Safety, Profit, Loss and Discount, Ratio and Proportion, Time and Work, Mensuration, Data Interpretation, Powers, Surds and Logarithms, Sequences and Series, Articles and Determiners, Sentence Completion, Data Sufficiency, Blood Relations, Simple Interest and Compound Interest, Mixture and Alligation, Sequence and Series (Series), Speed Time and Distance, Algebra, Profit and Loss, Powers and Exponents (Surds and Indices), Permutation and Combination
  2. General Awareness: Physics, Chemistry, Biology, History, Geography, Polity, Indian Economy, Environment, Static General Knowledge, GK- Current Affairs, Artificial Intelligence, MS Office Applications, Terms & Abbreviations, Keyboard Shortcuts, Evolution of Indian Banking (Banking & Financial Awareness), Emerging Tech Trends
  3. Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus, Probability, Statistics, Signal Space and Optimum Detection, Probability, Statistics
  4. Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep, Number Systems and Codes, Registers and Counters, Boolean Algebra and Logic Gates, Microprocessors and Microcontrollers, Logic Families and CMOS Logic, Microprocessors, Logic Gates and Boolean Algebra, Minimization of Boolean Functions, Timing, Hazards and Testing, Logic Families, Combinational Logic Design, Arithmetic Circuits, Waveform Generators and Timer Circuits, Semiconductor Memories and Programmable Logic Devices, Combinational Logic Circuits, Latches and Flip-Flops, Finite State Machines, Sequential Circuits and State Machines, Minimization of Boolean Functions, Arithmetic Circuits, Latches and Flip-Flops, Number Systems and Codes, Registers and Counters
  5. Computer Organisation & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer, Register Transfer and Microoperations, Semiconductor Memories and Programmable Logic, Processor Organization and Instructions, Memory Hierarchy and Input/Output, Registers and Counters
  6. Programming & Data Structures: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, HTML Basics, OOPS with C++, Java, Object Oriented Technology
  7. Databases: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, Database Security & Authorization
  8. Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  9. Theory of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory
  10. Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
  11. Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Security, Windows OS, Distributed Systems, Unix OS, Linux OS
  12. Computer Networks: Introduction to CN, 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, Data Communication, Website, Browser & Services, Web Design & Development, Network Security, Cyber Threats and Malware Attacks, Cyber Safety and Security
  13. Full Length Mock Tests:
  14. Sectional Tests:
  15. Paper 2 - Full-length Mock Tests:
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.

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