Functie derivabila

Post by **Beniamin Bogosel** » Thu May 22, 2008 7:11 pm

Determinati toate functiile derivabile \( f:\mathbb{R}\to \mathbb{R} \) cu \( f\circ f=f \).

Post by **Beniamin Bogosel** » Tue Aug 12, 2008 8:54 am

Derivam relatia si avem \( f^\prime (f(x)) f^\prime (x)=f^\prime(x),\ \forall x \in \mathbb{R} \). Facem \( x \to f(x) \) si folosim enuntul: \( (f^\prime(f(x)))^2=f^\prime(f(x)),\ \forall x \in \mathbb{R} \). Deoarece compusa a doua functii cu proprietatea lui Darboux are proprietatea lui Darboux si \( f^\prime(f(x))\in \{0,1\},\ \forall x \in \mathbb{R} \) rezulta ca \( f^\prime(f(x))=0,\ \forall x \in \mathbb{R} \) sau \( f^\prime(f(x))=1,\ \forall x \in \mathbb{R} \).

De aici, mai e putin...