inverse function

English

Pronunciation

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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→Y, a function g:Y→X such that, ∀x∈X, f(x)=y⟹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, 2nd edition, Wiley, page 51:
      An example of another function that has an inverse function is f(x)=4x+5.
      Its inverse is f−1(x)=x−54.
    • 2014, Mark Ryan, Calculus For Dummies, Wiley, 2nd Edition, page 147,
      If f and g are inverse functions, then
      f′(x)=1g′(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)

Translations

Further reading

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