document.write( "Question 1051337: How do you show if these equations are odd, even, or neither?\r
\n" ); document.write( "\n" ); document.write( "f(x)=x^3-8x f(x)=3x^4-7x+2\r
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Algebra.Com's Answer #666878 by ikleyn(52803) $\"\"$ $\"About$

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How do you show if these equations are odd, even, or neither?\r
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document.write( "1.  f(x) = x^3 - 8x\r\n" );
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document.write( "    To decide if it is odd, even, or neither, we must to consider f(-x) and compare it with f(x).\r\n" );
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document.write( "    f(-x) = (-x)^3 - 8*(-x).\r\n" );
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document.write( "    It is equal to \r\n" );
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document.write( "    f(-x) = (-x)^3 - 8*(-x) = -x^3 + 8x = -(x^3 -8).\r\n" );
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document.write( "    What is the very right side expression? It is nothing else as -f(x).\r\n" );
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document.write( "    So, we got f(-x) = -f(x).\r\n" );
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document.write( "    It means that the function f(x) is ODD.\r\n" );
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document.write( "2.  If you do the same with the function \"N2\", you will get that that this function is neither even nor odd.\r\n" );
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