inverse function
Noun

inverse function (plural inverse functions)

  1. (mathematics) For a given function f, another function, denoted f−1, that reverses the mapping action of f; (formally) given a function f: X\rightarrow Y, a function g: Y\rightarrow X such that, \forall x\in X,\ f(x) = y \implies g(y)=x.
    Halving is the inverse function of doubling.
    If an inverse function exists for a given function, then it is unique.
    The inverse function of an inverse function is the original function.
    • 1995, Nicholas M. Karayanakis, Advanced System Modelling and Simulation with Block Diagram Languages, CRC Press, page 217 ↗,
      In the context of linearization, we recall the reflective property of inverse functions; the ƒ curve contains the point (a,b) if and only if the ƒ -1 curve contains the point (b,a).
    • 2014, Mary Jane Sterling, Trigonometry For Dummies, Wiley, 2nd Edition, page 51 ↗,
      An example of another function that has an inverse function is f(x)=4x+5.
      Its inverse is f^{-1}(x)=\frac{x-5}{4}.
    • 2014, Mark Ryan, Calculus For Dummies, Wiley, 2nd Edition, page 147 ↗,
      If f and g are inverse functions, then
      f'(x)=\frac{1}{g'(f(x))}
      In words, this formula says that the derivative of a function, f, with respect to x, is the reciprocal of the derivative of its inverse function with respect to f.
Synonyms
  • (function that reverses the mapping action of a given function) anti-function (obsolete or nonstandard in this sense)
Related terms Translations
  • French: fonction réciproque
  • German: Umkehrfunktion, inverse Funktion
  • Italian: funzione inversa
  • Portuguese: função inversa
  • Russian: обратная фу́нкция
  • Spanish: función recíproca, función inversa



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