document.write( "Question 146271:
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Algebra.Com's Answer #106816 by Edwin McCravy(20056) $\"\"$ $\"About$
You can put this solution on YOUR website!
Please find the domain of $\"H%28x%29=sqrt%2825-x%5E2%29\"$
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document.write( "Note that  means the same as ,\r\n" );
document.write( "with the index  understood.\r\n" );
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document.write( "If a radical has an even index, that is:\r\n" );
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document.write( ", such as , , , etc.\r\n" );
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document.write( "then what is under the radical must not be negative.\r\n" );
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document.write( "Non-negative means \"positive or 0\", and \"positive\" means \"greater that 0\",\r\n" );
document.write( "therefore what is under the radical must be greater than or equal to 0.\r\n" );
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document.write( "So we make an inequality that says  is greater than or equal to 0.\r\n" );
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document.write( "We find all critical values by setting the left side = 0:\r\n" );
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document.write( "                              \r\n" );
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document.write( "                              ,\r\n" );
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document.write( "So we draw a number line and mark those numbers\r\n" );
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document.write( "<----------o-----------------------------o--------->\r\n" );
document.write( " -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8\r\n" );
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document.write( "Next we choose a number left of -5, say -6.\r\n" );
document.write( "Substitute it in the original inequality:\r\n" );
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document.write( "This is false so we do not shade to the left of -5.\r\n" );
document.write( "We still have this number line. \r\n" );
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document.write( "<----------o-----------------------------o--------->\r\n" );
document.write( " -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8\r\n" );
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document.write( "Next we choose a number right of -5 but left of 5, say 0.\r\n" );
document.write( "Substitute it in the original inequality:\r\n" );
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document.write( "This is true so we do shade to the line between -5 and +5,\r\n" );
document.write( "like this:\r\n" );
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document.write( "<----------o=============================o--------->\r\n" );
document.write( " -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8\r\n" );
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document.write( "Next we choose a number right of 5, say 6.\r\n" );
document.write( "Substitute it in the original inequality:\r\n" );
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document.write( "This is false so we do not shade to the right of 5.  \r\n" );
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document.write( "Next we must test the critical values in the original inequality\r\n" );
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document.write( "Testing \r\n" );
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document.write( "This is true so we darken the circle at -5.\r\n" );
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document.write( "<----------@=============================o--------->\r\n" );
document.write( " -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8\r\n" );
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document.write( "Testing \r\n" );
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document.write( "This is also true so we also darken the circle at 5.\r\n" );
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document.write( "<----------@=============================@--------->\r\n" );
document.write( " -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8\r\n" );
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document.write( "The interval notation for that is the abbreviation \r\n" );
document.write( "for the above number line graph:  \r\n" );
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document.write( "               [-5,-5]\r\n" );
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document.write( "Edwin
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