document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=389690>Question 389690</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Without graphing, find the domain of the following functions:\r<BR>\n" );
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document.write( "a)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+sqrt%28%28x+-+3%29%2F%282x%5E2+-+8%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+sqrt%28%28x+-+3%29%2F%282x%5E2+-+8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and\r<BR>\n" );
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document.write( "b)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+root%283%2C%28x+%2B+5%29%2F%28x%5E2+-+9%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+root%283%2C%28x+%2B+5%29%2F%28x%5E2+-+9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #276327 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=276327\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) Since there is a square root symbol, we have to ensure that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+3%29%2F%282x%5E2+-+8%29%3E=0 ALIGN=MIDDLE  ALT=\"%28x+-+3%29%2F%282x%5E2+-+8%29%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  To find the critical numbers, determine all x values that make either the top or the bottom equal to 0. By inspection they are -2, 2, and 3. These critical numbers partition the real number line into 4 parts.  Choosing the test numbers -3, 0, 2.5, and 4, and checking for the signs:<BR>\n" );
document.write( "For (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >, -2), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+3%29%2F%282x%5E2+-+8%29+%3C+0 ALIGN=MIDDLE  ALT=\"%28x+-+3%29%2F%282x%5E2+-+8%29+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "For (-2, 2), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+3%29%2F%282x%5E2+-+8%29%3E0 ALIGN=MIDDLE  ALT=\"%28x+-+3%29%2F%282x%5E2+-+8%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "For (2,3), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+3%29%2F%282x%5E2+-+8%29%3C+0 ALIGN=MIDDLE  ALT=\"%28x+-+3%29%2F%282x%5E2+-+8%29%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "For (3, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >), <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+3%29%2F%282x%5E2+-+8%29%3E+0 ALIGN=MIDDLE  ALT=\"%28x+-+3%29%2F%282x%5E2+-+8%29%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  <BR>\n" );
document.write( "Of the critical numbers, only 3 can be accepted, and not 2 and -2.  Therefore the domain is (-2, 2)U [3, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >).\r<BR>\n" );
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document.write( "b)  The radical symbol is a cube-root symbol, and every real number has a cube root (whether positive or negative).  Then the only thing we have to ensure is that the denominator won't be 0. The x-values that make the denominator 0 are -3 and 3.  Hence the domain is the set of all real numbers except -3 and 3, or R\{-3, 3}. </SPAN>\n" );
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