document.write( "Question 1040827: If f(x+y) = f(x) + f(y) x€R and y€R then f(0) equals to what \n" ); document.write( "

Algebra.Com's Answer #655765 by ikleyn(52814) $\"\"$ $\"About$

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document.write( "Then \r\n" );
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document.write( "  f(x) = f(x+0)              ( <--- since x = x+0 )\r\n" );
document.write( "= f(x) + f(0)                ( <--- since f(x+y) = f(x) + f(y) )\r\n" );
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document.write( "Thus we get \r\n" );
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document.write( "  f(x) = f(x) + f(0).\r\n" );
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document.write( "Now distract f(x) from both sides. You will get\r\n" );
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document.write( "  0 = f(0),  or  f(0) = 0.\r\n" );
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document.write( "Answer.  Then f(0) = 0.\r\n" );
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