document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1088423>Question 1088423</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the domain of the function. <BR>\n" );
document.write( "Domain in the link: http://prntscr.com/fyqy26 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #702692 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=702692\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\"><BR>\n" );
document.write( "Given Function:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://image.prntscr.com/image/mvFZwy4kTcOyPT_lzHnZXA.png\"><BR>\n" );
document.write( "Note: If the image doesn't show up, then it's the function g(x) = 1/(x(x+2))\r<BR>\n" );
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document.write( "The domain is the set of numbers x where x can be any real number but it cannot be equal to zero, and it also can't be equal to -2<BR>\n" );
document.write( "Why can't x equal these values? Because either value makes the denominator x(x+2) equal to zero.\r<BR>\n" );
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document.write( "We can see this by solving x(x+2) = 0 for x<BR>\n" );
document.write( "x(x+2) = 0<BR>\n" );
document.write( "x(x+2) = 0<BR>\n" );
document.write( "x=0 or x+2 = 0<BR>\n" );
document.write( "x = 0 or x = -2\r<BR>\n" );
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document.write( "And we can check each value<BR>\n" );
document.write( "Plug in x = 0<BR>\n" );
document.write( "x(x+2) = 0<BR>\n" );
document.write( "0(0+2) = 0<BR>\n" );
document.write( "0(2) = 0<BR>\n" );
document.write( "0 = 0 \r<BR>\n" );
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document.write( "Plug in x = -2<BR>\n" );
document.write( "x(x+2) = 0<BR>\n" );
document.write( "-2(-2+2) = 0<BR>\n" );
document.write( "-2(0) = 0<BR>\n" );
document.write( "0 = 0\r<BR>\n" );
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document.write( "So that shows how x = 0 or x = -2 makes the denominator x(x+2) equal to zero.\r<BR>\n" );
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document.write( "In set builder notation, the domain would be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \{x|x\mathbb{R}, \ x \neq 0, \ x \neq -2\}\">\r<BR>\n" );
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document.write( "In interval notation, the domain would be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(-\infty, -2\right)\cup\left(-2, 0\right)\cup\left(0, \infty\right)\">\r<BR>\n" );
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document.write( "Effectively we're \"gluing\" three intervals together. Or put another way, we're poking holes in the number line at -2 and 0 while leaving any other number as part of the domain. <BR>\n" );
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