document.write( "Question 830346: What is the domain of the function h(x)=8x/(x(x^2-81))? \n" ); document.write( "

Algebra.Com's Answer #500540 by math-vortex(648) $\"\"$ $\"About$

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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "What is the domain of the function h(x)=8x/(x(x^2-81))?\r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "In this case you want to restrict from the domain of all real numbers, those values that make the denominator equal 0. (Division by zero is not defined.)\r\n" );
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document.write( "We simply set the denominator equal to zero and solve for x.\r\n" );
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document.write( "The expression {x^2-81}}} is the difference of two squares, and factors as (x-9)(x+9)\r\n" );
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document.write( "Then x = 0 OR x - 9 = 0 OR x + 9 = 0\r\n" );
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document.write( "x = 0 OR x = 9 OR x = -9\r\n" );
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document.write( "Consequently, the domain of the function h is all real numbers except -9, 0, and 9.\r\n" );
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document.write( "In bracket notation, we have\r\n" );
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document.write( "(-infinity,-9) U (-9,0) U (0, 9) U (9, infinity)\r\n" );
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document.write( "Hope this helps! Feel free to email if you have any questions about the solution.\r\n" );
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document.write( "Good luck with your math,\r\n" );
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document.write( "Mrs. F\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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