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Introduction to Inverse Functions definitions

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  • Function
    A relation pairing each input with at most one output, ensuring no input is linked to multiple outputs.
  • One-to-one Function
    A mapping where each output is paired with at most one input, confirmed by unique input-output pairs.
  • Inverse Function
    A function that reverses the original mapping, swapping inputs and outputs, denoted with a superscript negative one.
  • Ordered Pair
    A set of two values showing the correspondence between input and output, typically written as (x, y).
  • Input
    A value from the domain that is mapped to an output in a function, often represented as an x value.
  • Output
    A value from the range that results from applying a function to an input, often represented as a y value.
  • Domain
    The complete set of input values for a function, which becomes the range for its inverse.
  • Range
    The complete set of output values for a function, which becomes the domain for its inverse.
  • Horizontal Line Test
    A graphical method to verify one-to-one status by checking if any horizontal line crosses more than one point.
  • Vertical Line Test
    A graphical method to confirm a relation is a function by ensuring vertical lines cross at most one point.
  • Correspondence Diagram
    A visual representation using bubbles and arrows to show how inputs and outputs are paired in a function.
  • Mapping
    The process of associating each input with an output, illustrated by arrows or ordered pairs.
  • Notation
    A symbolic system, such as f⁻¹, used to represent mathematical concepts like inverse functions.