document.write( "Question 1208085: Determine if each function is even, odd or neither. \r
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\n" ); document.write( "\n" ); document.write( "A. F(x) = (x)^(1/3) + |x|^2\r
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\n" ); document.write( "\n" ); document.write( "B. G(x) = (1/x) - (x)^(1/4)\r
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\n" ); document.write( "\n" ); document.write( "C. H(x) = [(x)^(1/2) + 12x]/(x^3 - 9)\r
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\n" ); document.write( "\n" ); document.write( "D. S(x) = (x^4 + |x - 4|)/(x^4 - 2x) \n" ); document.write( "
Algebra.Com's Answer #846237 by ikleyn(52781)\"\" \"About 
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\n" ); document.write( "Determine if each function is even, odd or neither.\r
\n" ); document.write( "\n" ); document.write( "A. F(x) = (x)^(1/3) + |x|^2\r
\n" ); document.write( "\n" ); document.write( "B. G(x) = (1/x) - (x)^(1/4)\r
\n" ); document.write( "\n" ); document.write( "C. H(x) = [(x)^(1/2) + 12x]/(x^3 - 9)\r
\n" ); document.write( "\n" ); document.write( "D. S(x) = (x^4 + |x - 4|)/(x^4 - 2x)
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\n" ); document.write( "\n" ); document.write( "                I will answer  (B),  (C)  and  (D).\r
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document.write( "(B)  In (B),  (x)^(1/4)  is defined only for  x >= 0.\r\n" );
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document.write( "     Therefore, function G(x) is defined only for  x >= 0.\r\n" );
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document.write( "     Therefore, the conception of even and/or odd function is inapplicable for G(x).\r\n" );
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document.write( "     Therefore, the answer for (B) is \"neither\".\r\n" );
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document.write( "(C)  In (C),  (x)^(1/2)  is defined only for  x >= 0.\r\n" );
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document.write( "     Therefore, function H(x) is defined only for  x >= 0.\r\n" );
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document.write( "     Therefore, the conception of even and/or odd function is inapplicable for H(x).\r\n" );
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document.write( "     Therefore, the answer for (C) is \"neither\".\r\n" );
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document.write( "(D)  In (D), calculate  S(x) at two values of x: x= 1 and x= -1.\r\n" );
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document.write( "     At x= 1,  S(1)  = \"%281%5E4%2Babs%281-4%29%29%2F%281%5E4-2%2A1%29\" = \"%281%2B3%29%2F%281-2%29\" = \"4%2F%28-1%29\" = -4.\r\n" );
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document.write( "     At x= -1, S(-1) = \"%28%28-1%29%5E4%2Babs%28-1-4%29%29%2F%28%28-1%29%5E4-2%2A%28-1%29%29\" = \"%281%2B5%29%2F%281%2B2%29\" = \"6%2F3\" = 2.\r\n" );
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document.write( "     So, neither  S(1) = S(-1)  nor  S(1) = -S(-1).  Thus we conclude that function S(x) is neither even nor odd.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Parts  (B),  (C)  and  (D)  are solved and answered,  with explanations.\r
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