document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=151704>Question 151704</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need the domain of the following problem: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=5x%2Fx%5E2%2B25 ALIGN=MIDDLE  ALT=\"g%28x%29=5x%2Fx%5E2%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Please. College Algebra. If I can figure out the meaning of domain and see it being worked in a problem, I should be able to work it. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #111519 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=111519\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%285x%29%2F%28x%5E2%2B25%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%285x%29%2F%28x%5E2%2B25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B25=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B25=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=-25 ALIGN=MIDDLE  ALT=\"x%5E2=-25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 25 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%28-25%29 ALIGN=MIDDLE  ALT=\"x=sqrt%28-25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%28-1%29%2Asqrt%2825%29 ALIGN=MIDDLE  ALT=\"x=sqrt%28-1%29%2Asqrt%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-25%29 ALIGN=MIDDLE  ALT=\"sqrt%28-25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-1%29%2Asqrt%2825%29 ALIGN=MIDDLE  ALT=\"sqrt%28-1%29%2Asqrt%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=i%2Asqrt%2825%29 ALIGN=MIDDLE  ALT=\"x=i%2Asqrt%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with \"i\"\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5%2Ai ALIGN=MIDDLE  ALT=\"x=5%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5i ALIGN=MIDDLE  ALT=\"x=-5i\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of 25 to get 5 or -5\r<BR>\n" );
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document.write( "Since the values <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5%2Ai ALIGN=MIDDLE  ALT=\"x=5%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5i ALIGN=MIDDLE  ALT=\"x=-5i\"   DISABLED_style= \"max-width:90%; height:auto;\" > make the denominator zero, this means that there are no real x values that make the denominator zero (since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5i ALIGN=MIDDLE  ALT=\"5i\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5i ALIGN=MIDDLE  ALT=\"-5i\"   DISABLED_style= \"max-width:90%; height:auto;\" > are both complex). \r<BR>\n" );
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document.write( "So you can plug in any real number for x and you'll get a result for f(x). \r<BR>\n" );
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document.write( "If that doesn't make any sense to you, then try to think of it like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <font size=4><b>always</b></font> positive. So there are no real values that make <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=-25 ALIGN=MIDDLE  ALT=\"x%5E2=-25\"   DISABLED_style= \"max-width:90%; height:auto;\" > true. That's why the domain includes all real numbers.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the domain of the function in set-builder notation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{\left{x|x\in\mathbb{R}\right}}\">\r<BR>\n" );
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document.write( "In plain English, this reads: x is the set of all real numbers (In other words, x can be <b>any</b> number)\r<BR>\n" );
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document.write( "Also, in interval notation, the domain is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(-\infty,\infty \right)\">\r<BR>\n" );
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document.write( " </SPAN>\n" );
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