document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159882>Question 159882</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the doman of the function:\r<BR>\n" );
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document.write( "y=2 /  x-1 =\r<BR>\n" );
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document.write( "or y= 3x /  4 =  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117903 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=117903\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%282%29%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"y=%282%29%2F%28x-1%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-1=0 ALIGN=MIDDLE  ALT=\"x-1=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=0%2B1 ALIGN=MIDDLE  ALT=\"x=0%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >Add 1 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > makes the denominator equal to zero, this means we must exclude <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > from our domain\r<BR>\n" );
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document.write( "So our domain is:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \textrm{\left{x|x\in\mathbb{R} x\neq1\right}}\">\r<BR>\n" );
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document.write( "which in plain English reads: x is the set of all real numbers except x CANNOT equal <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our domain looks like this in interval notation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(-\infty, 1\right)\cup\left(1,\infty \right)\">\r<BR>\n" );
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document.write( "note: remember, the parenthesis <font size=4><b>excludes</b></font> 1 from the domain\r<BR>\n" );
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document.write( "# 2\r<BR>\n" );
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document.write( "Looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x%2F4 ALIGN=MIDDLE  ALT=\"y=3x%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can see that there are no square roots, logs, and other functions where there are restrictions on the domain.\r<BR>\n" );
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document.write( "Also, we can see that the function does not have a division by x (or any combination of variables and constants).<BR>\n" );
document.write( "So we don't have to worry about division by zero.\r<BR>\n" );
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document.write( "Since we don't have any restrictions on the domain, this shows us that the domain is all real numbers. In other words, we can plug in <b>any</b> number in for x\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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