document.write( "Question 210799: find the domain of function f(x) = root 2x - 3\r
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Algebra.Com's Answer #159259 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
find the domain of function $\"f%28x%29+=+sqrt%282x+-+3%29\"$
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document.write( "There are two ways, graphically and algebraically.\r\n" );
document.write( "I'll do the graphical way first.\r\n" );
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document.write( "First draw the graph of \r\n" );
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document.write( "consider the x-axis as a number line, shade the part\r\n" );
document.write( "that is directly underneath or above the curve. in \r\n" );
document.write( "this particular case the graph is entirely above the \r\n" );
document.write( "x-axis at and to the right of 1.5.  So shade the \r\n" );
document.write( "x-axis number line everywhere underneath the curve,\r\n" );
document.write( "putting a darkened circle at the start of the shading,\r\n" );
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document.write( "And so the number line that represents the domain is\r\n" );
document.write( "this number line:\r\n" );
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document.write( "which in interval notation is\r\n" );
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document.write( "and in set-builder notation is\r\n" );
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document.write( "   {x|x≧1.5}\r\n" );
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document.write( "To do it using only algebra:\r\n" );
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document.write( "No negative numbers can appear under square roots,\r\n" );
document.write( "fourth roots, sixth roots, eighth roots or EVEN\r\n" );
document.write( "roots in general.  (However negative numbers can\r\n" );
document.write( "appear under cube roots, fifth roots, and odd roots\r\n" );
document.write( "in general, but we only have an even root here.)\r\n" );
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document.write( "Therefore we must set what's under the square root\r\n" );
document.write( "radical, which is  greater than or equal to 0:\r\n" );
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document.write( "and solve that for x\r\n" );
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document.write( "Divide through by 3:\r\n" );
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document.write( "You can write it any of the above three ways.\r\n" );
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document.write( "So we shade that on a number line:\r\n" );
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document.write( "-3  -2  -1   0   1   2   3   4   5   6\r\n" );
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document.write( "That is the graph of the domain, which is the\r\n" );
document.write( "same as the x-axis shaded under the graph above.\r\n" );
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document.write( "which in interval notation, as above, is\r\n" );
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document.write( "and in set-builder notation is\r\n" );
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document.write( "   {x|x≧1.5}\r\n" );
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document.write( "Edwin

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