Determinati functia \( f:\mathbb{R}\rightarrow\mathbb{R} \) care verifica relatia: \( f\left(x-y\right)+f\left(2x-z\right)+f\left(y-z\right)=3\left(3x-2z+4\right) \).
Alfred Eckstein, Viorel Tudoran, G.M.-B. 12/2008
Ecuatie functioanala
Moderators: Bogdan Posa, Laurian Filip
-
Claudiu Mindrila
- Fermat
- Posts: 520
- Joined: Mon Oct 01, 2007 2:25 pm
- Location: Targoviste
- Contact:
Ecuatie functioanala
Last edited by Claudiu Mindrila on Mon Mar 02, 2009 9:44 pm, edited 1 time in total.
elev, clasa a X-a, C. N. "C-tin Carabella", Targoviste
functie G.M.
Pentru x=y=z=o obtinem f(0)=4 (1)
Pentru x=y=z=a avem 2f(0)+f(a)=3a+12 (2).
Din (1) si (2) obtinem imediat f(a)=3a+4. q.e.d
Pentru x=y=z=a avem 2f(0)+f(a)=3a+12 (2).
Din (1) si (2) obtinem imediat f(a)=3a+4. q.e.d