Iar o functie

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alex2008
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Iar o functie

Post by alex2008 »

Sa se afle functia \( f:\mathb{R}\rightarrow\mathb{R} \) astfel incat \( x\cdot f(x)+(1-x)\cdot f(-x)=x+1 \) , (\( \forall \))\( x\in\mathb{R} \)
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Laurian Filip
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Post by Laurian Filip »

\( \left\{\begin{array}{rcl} xf(x)+(1-x)f(-x)=x+1 \\
-xf(-x)+(1+x)f(x)=-x+1 \end{array}\right \)


\( x^2f(x)+(1-x^2)f(x)=2x^2-x+1 \)
\( f(x)=2x^2-x+1 \)
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