document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1117852>Question 1117852</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Look at this function: &#119891;(&#119909;) = ln(&#119909;^2 + 2&#119909; &#8722; 2).<BR>\n" );
document.write( "1.) What is the domain? <BR>\n" );
document.write( "2.) What are the equations of all asymptotes of &#119891;(&#119909;).<BR>\n" );
document.write( "3.) Find the solution set (solve) for the inequality &#119891;(&#119909;) &#8804; 0, write the solution set in interval notation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #733050 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=733050\">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 the function is the set of all real numbers excluding all values of the independent variable such that the argument of the natural logarithm function is less than or equal to zero.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(x)\ =\ \ln\(x^2\ +\ 2x\ -\ 2}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \text{dom}\(f\)\ =\ \{x\,\in\,\mathbb{R}\,|\,x^2\ +\ 2x\ -\ 2\ >\ 0\}\">\r<BR>\n" );
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document.write( "Vertical asymptotes are located where the independent variable equals a zero of the logarithm argument.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 2x\ -\ 2\ =\ 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ -1\ -\ \sqrt{3}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ -1\ +\ \sqrt{3}\">\r<BR>\n" );
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document.write( "The solution set for the inequality <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x)\ \leq\ 0\"> is the set of all values of the independent variable such that the argument of the logarithm function is in the interval (0,1].\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 2x\ -\ 2\ =\ 1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x\ -\ 1)(x\ +\ 3)\">\r<BR>\n" );
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document.write( "So the solution set for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x)\ \leq\ 0\"> is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \{x\,\in\,\mathbb{R}\,|\,-3\ \leq\ x\ <\ -1\ -\sqrt{3}\ \small{\vee}\LARGE\ -1\ +\ \sqrt{3}\ <\ x\ \leq\ 1\}\">\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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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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