Relations and Functions

IIT-JEE · Class 12 · Mathematics

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What’s covered

  • topics
    • Real Numbers and Inequalities
      • intervals as a subset of set R
      • inequalities
      • sign scheme method
      • modulus of a real number
      • modulus of addition and subtraction
    • Relations
      • domain range and codomain of a relation
      • number of relations
      • types of relation
    • Functions
      • domain codomain and range of a function
      • function as a relation between independent and dependent variables
      • vertical line test
      • elementary functions
      • identical functions
      • piecewise functions
      • algebra of functions
    • Types of Functions
      • one-one and many-one functions
      • onto and into functions
    • Standard Functions
      • algebraic and quadratic functions
      • trigonometric functions
      • inverse trigonometric functions
      • exponential and logarithmic functions
      • greatest integer function
      • fractional part function
      • signum function
      • maximum and minimum functions
    • Even and Odd Functions
      • even function
      • odd function
      • even and odd extension
    • Periodic Functions
      • period of elementary functions
      • period of transformed functions
      • period of composite functions
      • period from algebraic operations
    • Composite and Inverse Functions
      • injective and surjective nature of composite functions
      • inverse functions and their properties
    • Functional Equations
      • finding the value of a function
      • finding the function
      • properties of functions
    • Transformation of Graphs
      • vertical and horizontal shift
      • horizontal and vertical stretch or squeeze
      • vertical and horizontal flip
      • transformation related to modulus
      • graph involving the greatest integer function