Inverse of a Function

Duration: 5 min

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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:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a lecture on the mathematical concept of inverse functions. It begins by defining an inverse function as one that reverses the mapping of another function, specifically noting that if f(x) = y, then f^-1(y) = x. The instructor uses diagrams to illustrate the flow of inputs and outputs, emphasizing that a valid inverse requires a bijective (one-to-one and onto) relationship. The lecture transitions to a specific problem from the GATE 1996 exam, asking students to find the inverse of a function f: R x R -> R x R defined by f(x, y) = (x + y, x - y). The instructor demonstrates a method of verification by substituting specific values to test the given multiple-choice options, ultimately identifying the correct inverse function formula.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a slide titled 'Inverse of a function' which defines the concept as a function that 'reverses' another. The text states that if f(x) = y, then f^-1(y) = x. The instructor draws a diagram with two circles labeled A and B containing inputs x and y respectively. He draws an arrow from A to B labeled 'f' representing the function, and a return arrow from B to A labeled 'f^-1' representing the inverse. He further illustrates the concept of bijectivity by drawing cylinder-like diagrams with arrows. One diagram shows multiple arrows pointing to a single output, which he marks with an 'X' to indicate it does not have an inverse. Another diagram shows a one-to-one mapping, which is valid for inversion.

  2. 2:00 – 5:00 02:00-05:00

    The instructor presents a specific problem from GATE 1996 regarding a bijective function f: R x R -> R x R defined by f(x, y) = (x + y, x - y). The goal is to find the inverse function f^-1(x, y) from four options. He writes down the function definition and tests it with a specific input pair (3, 1), calculating the output as (3+1, 3-1) = (4, 2). He then sets up the inverse condition f^-1(4, 2) = (3, 1). He proceeds to test option (c), which is f^-1(x, y) = ((x + y) / 2, (x - y) / 2). By substituting x=4 and y=2 into this formula, he calculates ((4+2)/2, (4-2)/2) = (6/2, 2/2) = (3, 1). Since this matches the required input, he confirms option (c) is the correct answer.

  3. 5:00 – 5:11 05:00-05:11

    The video concludes with the instructor confirming the solution. The slide remains visible showing the problem statement and the four options, with option (c) clearly identified as the correct choice through the calculation shown. The instructor is visible in the bottom right corner, finalizing the explanation of the inverse function problem.

The lecture progresses from theoretical definitions to practical application. Initially, it establishes the fundamental definition of an inverse function, emphasizing the reversal of input and output values and the necessity of a bijective mapping for the inverse to exist. This theoretical foundation is then applied to a concrete problem involving a function on the set of real numbers. The instructor demonstrates a strategic approach to solving multiple-choice questions by using specific test values rather than algebraically deriving the inverse from scratch, verifying that the correct option maps the output back to the original input.

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