Page 1 of 1
Functie bijectiva
Posted: Mon Mar 02, 2009 6:30 pm
by dragosunguras
Fie \( f:[-\pi/2,\pi/2]\to\mathbb{R} \). Exista functii bijective f? Daca da, care ar fi acelea?
Posted: Mon Mar 02, 2009 10:47 pm
by DrAGos Calinescu
Tangenta, contangenta...
Posted: Mon Mar 02, 2009 11:14 pm
by enescu
DrAGos Calinescu wrote:Tangenta, contangenta...
Pai, nu sunt definite pe intervalul inchis
\( \left[ -\frac{\pi}{2},\frac{\pi}{2}\right] \), nu?
Posted: Tue Mar 03, 2009 12:43 pm
by dragosunguras
exact in asta consta, daca vreti ,dificultatea problemei ...pt ca e definita pe interval inchis
Posted: Tue Mar 03, 2009 12:55 pm
by Marius Mainea
\( [\frac{\pi}{2},\frac{\pi}{2}] \) si \( (\frac{\pi}{2},\frac{\pi}{2}) \) sunt cardinal echivalente( cardinalul lor se numeste puterea continuului) deci exista o functie bijectiva \( g:[\frac{\pi}{2},\frac{\pi}{2}]\rightarrow (\frac{\pi}{2},\frac{\pi}{2}) \)
Apoi functia cautata este \( \tan \circ g: [\frac{\pi}{2},\frac{\pi}{2}]\rightarrow \mathbb{R} \)