Functii frumoase

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alex2008
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Functii frumoase

Post by alex2008 »

Fie functiile \( f,g:\mathb{R}\rightarrow\mathb{R} \) astfel incat \( 2f(x)+f(1-y)+g(x)-g(y)=3(x+1)^2-6y \) , \( \forall x,y \in \mathb{R} \) si \( g(0)=0 \) . Sa se arate ca\( f(x)=g(x) \).
. A snake that slithers on the ground can only dream of flying through the air.
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Marius Mainea
Gauss
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Post by Marius Mainea »

Daca x=y in relatia din enunt obtinem \( 2f(x)+f(1-x)=3x^2+3 \). Prin inlocuirea lui x cu 1-x se determina f si apoi g.
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