document.write( "Question 1210376: find the domain and range of f(x) = (x)/(sqrt(1 - ((sqrt(- x)))^2)) \n" ); document.write( "
Algebra.Com's Answer #852134 by mccravyedwin(407)\"\" \"About 
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document.write( "find the domain and range of \"f%28x%29\"\"%22%22=%22%22\"\"%28x%5E%22%22%5E%22%22%29%2F%28sqrt%281+-+%28sqrt%28-x%29%29%5E2%29%29\"\r\n" );
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document.write( "x cannot be positive but can be 0. The denominator is always positive.\r\n" );
document.write( "So the value of f is never positive but can be 0 when x=0.\r\n" );
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document.write( "What is under the radical in the denominator must be positive, not negative or\r\n" );
document.write( "0.  Remember that -x can never be negative.\r\n" );
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document.write( "\"1-%28sqrt%28-x%29%29%5E2\"\"%22%22%3E%22%22\"\"0\"\r\n" );
document.write( "\"-%28sqrt%28-x%29%29%5E2\"\"%22%22%3E%22%22\"\"-1\"\r\n" );
document.write( "\"%28sqrt%28-x%29%29%5E2\"\"%22%22%3C%22%22\"\"1\"\r\n" );
document.write( "\"-x\"\"%22%22%3C%22%22%7B%7B%7B%22%22%3C%22%22\"\"1\"\r\n" );
document.write( "\"x\"\"%22%22%3E%22%22\"\"-1\"\r\n" );
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document.write( "Remember again that -x is non-negative. \r\n" );
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document.write( "\"-x\"\"%22%22=%22%22\"\"1\"\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"-1\" and since x is never positive but can be 0,\r\n" );
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document.write( "the domain is \"-1%3Cx%3C=0\"\r\n" );
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document.write( "We set the denominator = 0 to find the vertical asymptote:\r\n" );
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document.write( "\"sqrt%281+-+%28sqrt%28-x%29%29%5E2%29\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "\"1+-+%28sqrt%28-x%29%29%5E2\"\"%22%22=%22%22\"\"0\"\r\n" );
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document.write( "\"-%28sqrt%28-x%29%29%5E2\"\"%22%22=%22%22\"\"-1\"\r\n" );
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document.write( "\"%28sqrt%28-x%29%29%5E2\"\"%22%22=%22%22\"\"1\"\r\n" );
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document.write( "Remember that -x is non-negative. \r\n" );
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document.write( "\"-x\"\"%22%22=%22%22\"\"1\"\r\n" );
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document.write( "\"x\"\"%22%22=%22%22\"\"-1\"\r\n" );
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document.write( "So the vertical asymptote is \"x\"\"%22%22=%22%22\"\"-1\", indicated by the green line.\r\n" );
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document.write( "The domain is \"matrix%281%2C5%2C%22%28%22%2C-1%2C%22%2C%22%2C0%2C%22%5D%22%29\"\r\n" );
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document.write( "The range is \"matrix%281%2C5%2C%22%28%22%2C-infinity%2C%22%2C%22%2C0%2C%22%5D%22%29\"\r\n" );
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document.write( "Edwin
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