inverse function
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English
[edit]Noun
[edit]inverse function (plural inverse functions)
- (mathematics) For a given function f, another function, denoted f−1, that reverses the mapping action of f; (formally) given a function , a function such that, .
- 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 .
Its inverse is .
- 2014, Mark Ryan, Calculus For Dummies, Wiley, 2nd Edition, page 147,
- If and are inverse functions, then
- In words, this formula says that the derivative of a function, , with respect to , is the reciprocal of the derivative of its inverse function with respect to .
- If and are inverse functions, then
Synonyms
[edit]- (function that reverses the mapping action of a given function): anti-function (obsolete or nonstandard in this sense)
Related terms
[edit]Translations
[edit]function that reverses the mapping action of a given function
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Further reading
[edit]Bijection on Wikipedia.Wikipedia
Inverse function theorem on Wikipedia.Wikipedia
- Inverse function on Encyclopedia of Mathematics
- Inverse Function on Wolfram MathWorld