inverse function

Noun

 * 1)  For a given function f, another function, denoted f−1, that reverses the mapping action of f;  given a function $$f: X\rightarrow Y$$, a function $$g: Y\rightarrow X$$ such that, $$\forall x\in X,\ f(x) = y \implies g(y)=x$$.
 * 2) * 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 $$f$$.
 * 1) * 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 $$f$$.
 * 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 $$f$$.

Translations

 * Catalan: funció inversa
 * Czech: inverzní funkce
 * Danish: invers funktion, omvendt funktion
 * Finnish: käänteisfunktio
 * French: fonction réciproque
 * German:, inverse Funktion
 * Hungarian:
 * Italian:
 * Japanese:
 * Korean:
 * Latin: fūnctiō inversa
 * Norwegian:
 * Bokmål: invers funksjon
 * Nynorsk: invers funksjon
 * Polish: funkcja odwrotna
 * Portuguese: função inversa
 * Russian: обратная фу́нкция
 * Serbo-Croatian:
 * Cyrillic: инверзна функција
 * Roman: inverzna funkcija
 * Slovak: inverzná funkcia
 * Slovene: inverzna funkcija
 * Spanish: función recíproca, función inversa
 * Swedish: invers funktion
 * Tagalog: baligtad na kabisa
 * Ukrainian: обернена функція