document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=340924>Question 340924</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x)=sqrt(x+1/x-5) the domain is (-infinity,-1)u(5,infinity) does the inequality sign on the top of the fraction point the opposit way.  When solving I started out with x+1>or equal to 0 and x-5>or equal to 0 so my answer was <BR>\n" );
document.write( "(-1,5)u(5,infinity) where did I go wrong?  Are all functions able to be solved to discover their domain or is it a guessing game? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #244189 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=244189\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You have a function that involves both a radical with an even index (square root in this case) and a rational function (one expression divided by another).  You must restrict your domain such that the expression under the radical is greater than or equal to zero and you must also restrict it so that the denominator of the rational expression does not equal zero.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Restricting the denominator of the rational part of your function is simple in this case.  You simply cannot let the value of your independent variable, (<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">), be equal to 5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Restricting the radicand to zero or positive is a bit more complex.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note that if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ <\ -1\"> both denominator and numerator are negative, so the entire rational expression is positive.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ -1\">, then the rational expression equals zero.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ >\ -1\"> but <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ <\ 5\">, the denominator is positive but the numerator remains negative making the entire rational expression negative.  This becomes the interval that must be restricted on the basis of maintaining a positive or zero radicand.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 5\"> then the denominator of the rational expression becomes zero, hence this value must be restricted from the domain.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ > 5\"> then both numerator and denominator of the rational expression are positive, and the entire radicand is positive.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In summary, the domain is -1 or anything smaller and anything larger than 5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hence, in interval notation:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \"><font size\"+5\">(<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\infty\">,<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -1\ \ \">]<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large\ \ \cup\ \ \Large \left(5,\infty\right)\"></font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice the bracket vice parentheses on the -1 end of the first interval.  That includes the -1 endpoint as opposed to use of the parentheses on the 5 end of the second interval where we want to exclude the endpoint 5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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" );
document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://www.evolvefish.com/fish/media/E-FlyingSpaghettiEmblem.gif\"><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );