document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=629043>Question 629043</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the domain\r<BR>\n" );
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document.write( "y=&#8730;60x-25x^2-36\r<BR>\n" );
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document.write( "Please note that the square root sign cover not just 60x but 60x-25^2-36.\r<BR>\n" );
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document.write( "y=&#8730;5x^2+6x+1+1/3x+5\r<BR>\n" );
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document.write( "Please note again that the square root sign cover 5x^2+6x+1. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #395996 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=395996\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "The domain of a function is the set of all values of the independent variable for which the function exists.\r<BR>\n" );
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document.write( "The square root function exists mapped to the real numbers for all values of the independent variable for which the radicand is greater than or equal to zero.\r<BR>\n" );
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document.write( "Set up the inequality:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -25x^2\ +\ 60x\ -\ 36\ \geq\ 0\">\r<BR>\n" );
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document.write( "I'll leave it as an exercise for you to demonstrate that there is exactly one value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> for which this inequality is true, and hence the domain consists of this single value.\r<BR>\n" );
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document.write( "On the other hand, if you map the function to the complex numbers, then the domain is all reals, thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \text{dom}\left(y\ :\ \mathbb{R}\,\rightarrow\,\mathbb{C},\ y(x)\ =\ \sqrt{60x\ -\ 25x^2\ -\ 36}\right)\ =\ \left{x\ \in\ \mathbb{R}\right}\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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