document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=235932>Question 235932</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the domain of the function\r<BR>\n" );
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document.write( "p(x)=x^ - 2x +10\r<BR>\n" );
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document.write( "x^ means x squared, I hope I put that in right\r<BR>\n" );
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document.write( "thank you for your help, can wait to see the steps to this </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #173709 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=173709\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "The domain of a function is the set of values of the independent variable for which the function is defined.  What this means is that if you have a number that you would like to substitute for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> in your function <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p(x)\ =\ x^2\ -\ 2x\ +\ 10\"> and a real value for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p(x)\"> results, then the value you selected for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> IS in the domain set.  On the other hand, if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p(x)\"> is not defined for that value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">, then that value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> IS NOT in the domain.\r<BR>\n" );
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document.write( "Examining the given function, we can see that there are no instances of the independent variable in a denominator.  If that were the case, then we would have to exclude any value of the independent variable that would make any denominator equal to zero -- and hence make the entire function undefined.  We also have no radicals with even-numbered indices, so we do not have the problem of trying to take the square or higher even numbered root of a negative number.  There are also no logarithmic, trigonometric, or inverse trigonometric functions that might cause us to have domain restrictions.\r<BR>\n" );
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document.write( "In short, the domain of this function, namely <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p(x)\ =\ x^2\ -\ 2x\ +\ 10\"> is the set of all real numbers.  This can be expressed in interval notation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(-\infty,\,\infty\right)\">\r<BR>\n" );
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document.write( "Or set builder notation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \{x\,|\,x\,\in\,\R\}\">\r<BR>\n" );
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document.write( "In general, any polynomial equation of the form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ p(x)\ =\ a_nx^n\ +\ a_{n-1}x^{n-1}\ +\ a_{n-2}x^{n-2}\ +\ \cdots\ +\ a_0x^0\">\r<BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a_0\"> through <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a_n\"> are constant coefficients) has a domain of all real numbers, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(-\infty,\,\infty\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" );
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