document.write( "Question 1174552: Function f satisfies f(x)+2f(5-x)=x for all real numbers x. What is the value of f(1)? \n" ); document.write( "

Algebra.Com's Answer #799968 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "Function f satisfies f(x)+2f(5-x)=x for all real numbers x. What is the value of f(1)?
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document.write( "At x= 1 you have  f(1) + 2f(4) = 1    (1)\r\n" );
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document.write( "at x= 4 you have  f(4) + 2f(1) = 4    (2)\r\n" );
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document.write( "Write it as the 2x2-system of linear equations in STANDARD form\r\n" );
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document.write( "     f(1) + 2f(4) = 1     (1')\r\n" );
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document.write( "    2f(1) +  f(4) = 4     (2')\r\n" );
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document.write( "Multiply equation (2') by 2;  keep equation (1') as is\r\n" );
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document.write( "     f(1) + 2f(4) = 1     (1'')\r\n" );
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document.write( "    4f(1) + 2f(4) = 8     (2'')\r\n" );
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document.write( "From equation ((2''), subtract equation (1'')\r\n" );
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document.write( "     3f(1)        = 7\r\n" );
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document.write( "      f(1)        = .      ANSWER\r\n" );
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