document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=98069>Question 98069</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a polynomial and rational inequality problem. The problem is<BR>\n" );
document.write( "f(x)= 7x(squared)-59x+24  (the equation has the square root symbol throughout.  The question is \"what is the domain?\" </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #71356 by </B><A HREF=/tutors/aboutme.mpl?userid=mathslover><B>mathslover(157)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathslover><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=mathslover><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=71356\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> F(x)= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%287x%5E2+-59x+%2B24%29 ALIGN=MIDDLE  ALT=\"+sqrt%287x%5E2+-59x+%2B24%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the domain of the function is x such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%5E2+-59x+%2B24+%3E=0 ALIGN=MIDDLE  ALT=\"7x%5E2+-59x+%2B24+%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "using middle term factorisation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7x%5E2+-+56x+-+3x+-24+%3E=0 ALIGN=MIDDLE  ALT=\"+7x%5E2+-+56x+-+3x+-24+%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7x%28x-8%29+-3%28x-8%29+%3E=0 ALIGN=MIDDLE  ALT=\"+7x%28x-8%29+-3%28x-8%29+%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-8%29%287x-3%29%3E=0 ALIGN=MIDDLE  ALT=\"%28x-8%29%287x-3%29%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now the left hand side expression of the inequality will be greater than or<BR>\n" );
document.write( "equal to 0 when both the factors are greater than or equal to 0 or both of them are less than or equal to zero\r<BR>\n" );
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document.write( "so we have<BR>\n" );
document.write( "x-8>=0 and 7x-3>=0<BR>\n" );
document.write( "x>=8 and x>=3/7<BR>\n" );
document.write( "so in effect what it means is that x should be >=8 and x >=3/7<BR>\n" );
document.write( "which would combine to give one condition x>=8\r<BR>\n" );
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document.write( "also <BR>\n" );
document.write( "x-8<=0 and 7x-3<=0<BR>\n" );
document.write( "x<=8 and x<=7/3<BR>\n" );
document.write( "this would combine to give x<=7/3\r<BR>\n" );
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document.write( "so the domain is {x<=7/3} U {x>=8}  </SPAN>\n" );
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