Državno natjecanje 1996 SŠ2 1
Dodao/la:
arhiva1. travnja 2012. Ako funkcija
![f](/media/m/9/9/8/99891073047c7d6941fc8c6a39a75cf2.png)
zadovoljava uvjete
a)
![f\!\left(1\right) = 1](/media/m/2/a/d/2adaaed9fc11e501ca6b853507d3e3cc.png)
b)
![f\!\left(x+y\right) = f\!\left(x\right) + f\!\left(y\right)](/media/m/1/e/b/1eb3caf752355b0c664a2a2effe3b03f.png)
,
![\forall x,\,y \in \mathbb{R}](/media/m/4/f/6/4f6733ac356bd43cc0fffe9181dc93ed.png)
c)
![\displaystyle f\!\left(\frac1x\right) = \frac{f\!\left(x\right)}{x^2}](/media/m/1/b/5/1b598454519f6c86b962f5717a6b158b.png)
,
![\forall x \in \mathbb{R}](/media/m/f/6/4/f6452048baf87849bd440f525fb9c0a5.png)
,
![x \neq 0](/media/m/7/2/0/720c60218a1615ed1f02893e00659bbc.png)
koliko je
![f\!\left(\sqrt{1996}\right)](/media/m/f/2/7/f27625bef60df1b71184a4bcca48ba44.png)
?
%V0
Ako funkcija $f$ zadovoljava uvjete
a) $f\!\left(1\right) = 1$
b) $f\!\left(x+y\right) = f\!\left(x\right) + f\!\left(y\right)$, $\forall x,\,y \in \mathbb{R}$
c) $\displaystyle f\!\left(\frac1x\right) = \frac{f\!\left(x\right)}{x^2}$, $\forall x \in \mathbb{R}$, $x \neq 0$
koliko je $f\!\left(\sqrt{1996}\right)$?
Izvor: Državno natjecanje iz matematike 1996