document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=178169>Question 178169</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What values of x are excluded for the function f(x) = (x-1)/(x^2+1)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #133131 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=133131\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+1\">\r<BR>\n" );
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document.write( "The values of <i><b>x</b></i> that are excluded are any values that would cause the denominator to be zero.\r<BR>\n" );
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document.write( "So take the denominator of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x) = {(x-1) \over (x^2+1)}\">\r<BR>\n" );
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document.write( "and set it equal to zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^2 + 1 = 0\"> which has no solutions over the real numbers.  Hence, the domain of <i><b>f</b></i> is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \{x | x \in \R\}\">\r<BR>\n" );
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document.write( "Compare with <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large g(x) = {(x-1) \over (x^2-1)}\">\r<BR>\n" );
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document.write( "Here setting the denominator equal to zero yields:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x^2 - 1 = 0\">\r<BR>\n" );
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document.write( "which has two real solutions, namely 1 and -1.  Therefore the the domain of <i><b>g</b></i> is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \{x | x \in \R\, x \neq 1, x \neq -1}\">\r<BR>\n" );
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document.write( "</font> </SPAN>\n" );
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