document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1001695>Question 1001695</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the domain of the function.\r<BR>\n" );
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document.write( "f(x)= ln(x^2-9 / x^2+9x+14) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #618778 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52803)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=618778\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "You need to determine where the function under the logarithm, \r<BR>\n" );
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document.write( "f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-9%29%2F%28x%5E2+%2B+9x+%2B+14%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-9%29%2F%28x%5E2+%2B+9x+%2B+14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;is greater than zero, &nbsp;f(x) > 0.\r<BR>\n" );
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document.write( "Notice that &nbsp;1) &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-9%29= ALIGN=MIDDLE  ALT=\"x%5E2-9%29=\"   DISABLED_style= \"max-width:90%; height:auto;\" > = (x+3)*(x-3), &nbsp;and &nbsp;2) &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+9x+%2B+14 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+9x+%2B+14\"   DISABLED_style= \"max-width:90%; height:auto;\" > = (x+2)*(x+7). &nbsp;&nbsp;&nbsp;&nbsp;Therefore, \r<BR>\n" );
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document.write( "f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B3%29%2A%28x-3%29%29%2F%28%28x%2B7%29%2A%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"%28%28x%2B3%29%2A%28x-3%29%29%2F%28%28x%2B7%29%2A%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now, &nbsp;f(x) > 0 \r<BR>\n" );
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document.write( "1) &nbsp;in the semi-infinite interval &nbsp;x < -7, &nbsp;or &nbsp;(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >);\r<BR>\n" );
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document.write( "2) &nbsp;in the interval &nbsp;-3 < x < -2, &nbsp;or &nbsp;(-3, -2);\r<BR>\n" );
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document.write( "3) &nbsp;in the semi-infinite interval &nbsp;x > 3, &nbsp;or &nbsp;(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\r<BR>\n" );
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document.write( "See the plots below.\r<BR>\n" );
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document.write( "  <TR>\r\n" );
document.write( "  <TD > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+330%2C+330%2C+-12.5%2C+6.5%2C+-11.5%2C+8.5%2C%0D%0A+++++++++++%28x%5E2-9%29%2F%28x%5E2+%2B+9x+%2B+14%29%2C%0D%0A+++++++++++x%5E2+-9%2C+x%5E2+%2B+9x+%2B+14%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<B>Figure</B>. Plot f(x) (red line);<BR>\n" );
document.write( "plot of the numerator (green line);<BR>\n" );
document.write( "plot of denominator (blue line).\r<BR>\n" );
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document.write( "  </TD>\r\n" );
document.write( "  </TR>\r\n" );
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document.write( "</TABLE><BR>\n" );
document.write( " </SPAN>\n" );
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