document.write( "Question 975009: what is the domain of: \"+sqrt%28+15x%2F%28x%5E2-1%29+%29+\" \n" ); document.write( "
Algebra.Com's Answer #596832 by ikleyn(52803)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "The domain for this function is the set of real numbers where the expression under the square root is defined and is greater or equal to zero (is non-negative):\r
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\n" ); document.write( "\n" ); document.write( "\"x%2F%28x%5E2-1%29\" >= \"0\".\r
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\n" ); document.write( "\n" ); document.write( "The numbers  \"x+=+1\"  and  \"x+=+-1\"  are not in the domain because the function is not defined for these values. \r
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\n" ); document.write( "\n" ); document.write( "Further,  the expression  \"x%2F%28x%5E2-1%29\"  is positive if and only if the numerator and denominator are both positive at the same time   OR   are both negative at the same time. \r
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\n" ); document.write( "\n" ); document.write( "The numerator and denominator are both positive at the same time if the following inequalities are held:  \"x\" >= \"0\"   AND   \"abs%28x%29\" > 1.\r
\n" ); document.write( "\n" ); document.write( "    These two inequalities are valid in the domain  \"x\" > 1. \r
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\n" ); document.write( "\n" ); document.write( "The numerator and denominator are both negative at the same time if the following inequalities are held:  \"x\" <= \"0\"   AND   \"abs%28x%29\" < 1.\r
\n" ); document.write( "\n" ); document.write( "    These two inequalities are valid in the domain  \"-1\" < \"x\" <= \"0\". \r
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\n" ); document.write( "\n" ); document.write( "Answer.  The function  \"sqrt%28x%2F%28x%5E2-1%29%29\"  has the domain  \"-1\" < \"x\" <= \"0\"   and    \"x\" > 1   (the union of two sub-domains).\r
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