inverse function
Noun
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Noun
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 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.
- If f and g are inverse functions, then
- (function that reverses the mapping action of a given function) anti-function (obsolete or nonstandard in this sense)
- French: fonction réciproque
- German: Umkehrfunktion, inverse Funktion
- Italian: funzione inversa
- Portuguese: função inversa
- Russian: обратная фу́нкция
- Spanish: función recíproca, función inversa
This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.002