Functie bijectiva

dragosunguras · Post by **dragosunguras** » Mon Mar 02, 2009 6:30 pm

Fie \( f:[-\pi/2,\pi/2]\to\mathbb{R} \). Exista functii bijective f? Daca da, care ar fi acelea?

DrAGos Calinescu · Post by **DrAGos Calinescu** » Mon Mar 02, 2009 10:47 pm

Tangenta, contangenta...

enescu · Post by **enescu** » Mon Mar 02, 2009 11:14 pm

DrAGos Calinescu wrote:Tangenta, contangenta...

Pai, nu sunt definite pe intervalul inchis \( \left[ -\frac{\pi}{2},\frac{\pi}{2}\right] \), nu?

dragosunguras · Post by **dragosunguras** » Tue Mar 03, 2009 12:43 pm

exact in asta consta, daca vreti ,dificultatea problemei ...pt ca e definita pe interval inchis

Marius Mainea · Post by **Marius Mainea** » Tue Mar 03, 2009 12:55 pm

\( [\frac{\pi}{2},\frac{\pi}{2}] \) 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 \( \tan \circ g: [\frac{\pi}{2},\frac{\pi}{2}]\rightarrow \mathbb{R} \)