document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=286185>Question 286185</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the domain of the function g(x)=8 'over' 2-3x<BR>\n" );
document.write( "I'm so lost...Thank you in advance!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #207512 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=207512\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Reminder: The domain is the set of all allowable inputs. You can think of this as the set of all possible 'x' values (that produce some number as an output).\r<BR>\n" );
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document.write( "Remember that you CANNOT divide by zero. So if the denominator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-3x=0 ALIGN=MIDDLE  ALT=\"2-3x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2F3 ALIGN=MIDDLE  ALT=\"x=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (solve for 'x'). This means that if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2F3 ALIGN=MIDDLE  ALT=\"x=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-3x=0 ALIGN=MIDDLE  ALT=\"2-3x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "In other words, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2F3 ALIGN=MIDDLE  ALT=\"x=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the denominator is zero (which is not allowed). So we must exclude this value from the domain. Since there are no other values that make the denominator zero, this means that the only value to exclude from the domain is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2F3 ALIGN=MIDDLE  ALT=\"x=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the domain is the set of all real numbers except <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E2%2F3 ALIGN=MIDDLE  ALT=\"x%3C%3E2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We denote this in interval notation as  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-\infty,\frac{2}{3}\right)\cup\left(\frac{2}{3},\infty\right)\">\r<BR>\n" );
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document.write( "Basically, this is the interval <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(-\infty,\infty\right)\"> with the number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > taken out of it. </SPAN>\n" );
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