+0  
 
 #1
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0

-1 is the answer

 Nov 26, 2019
 #2
avatar+23841 
+3

The function \(f(x)\) satisfies \(f(x) + 2f(1 - x) = 3x^2\) for all real numbers \(x\).
Find \(f(3)\).

 

\(\begin{array}{|l|rcll|} \hline x=-2: & f(-2) + 2f\Big(1 - (-2)\Big) &=& 3(-2)^2 \\ & \color{blue}f(-2) + 2f(3) &\color{blue}=& \color{blue}12 \\ & \mathbf{f(-2)} &=& \mathbf{12-2f(3)} \\\\ x=3: & f(3) + 2f(1 - 3) &=& 3(3)^2 \\ & \color{blue}f(3) + 2f(-2) &\color{blue}=& {\color{blue}27} \quad | \quad \mathbf{f(-2)=12-2f(3)} \\ & f(3) + 2\Big(12-2f(3)\Big) &=& 27 \\ & f(3) + 24 -4f(3)&=& 27 \\ & -3f(3) &=& 27 - 24 \\ & -3f(3) &=& 3 \quad | \quad :(-3) \\ & \mathbf{f(3)} &=& \mathbf{-1} \\ \hline \end{array}\)

 

laugh

 Nov 26, 2019
edited by heureka  Nov 26, 2019
 #3
avatar+106533 
0

Very nice, heureka    !!!!

 

 

cool cool cool

CPhill  Nov 26, 2019

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