document.write( "Question 765689: how do i know if f(x)= x/6 is a function.
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Algebra.Com's Answer #467142 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "For contradiction we assume f(x) is NOT a function.\r\n" );
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document.write( "Then there must be two different outputs for the same input,\r\n" );
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document.write( "Let a be the input and b and c be the two different outputs, b ≠ c.\r\n" );
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document.write( "Then (a,b) and (a,c) are both elements of the relation where b ≠ c.\r\n" );
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document.write( "Let y = f(x) = \r\n" );
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document.write( "Solve y =  for x\r\n" );
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document.write( "     6y = x\r\n" );
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document.write( "Substitute (a,b) and (a,c)\r\n" );
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document.write( "   6b = a,     6c = a\r\n" );
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document.write( "then 6b = 6c\r\n" );
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document.write( "      b = c.\r\n" );
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document.write( "That contracts the assumption that b ≠ c\r\n" );
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document.write( "Therefore the assumption that f(x) is not a function\r\n" );
document.write( "is false, and therefore f(x) is a function.\r\n" );
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document.write( "Edwin

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