document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177051>Question 1177051</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the domain and range of A): 1/(√(3-2x-x^2))<BR>\n" );
document.write( "B): 1/(√(x^2+2x+3)) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #805302 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=805302\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Find the domain and range of \r<BR>\n" );
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document.write( "A): \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2F%28sqrt%283-2x-x%5E2%29%29 ALIGN=MIDDLE  ALT=\"y=1%2F%28sqrt%283-2x-x%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "domain: exclude all values of x that make denominator equal to zero\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283-2x-x%5E2%29=0 ALIGN=MIDDLE  ALT=\"sqrt%283-2x-x%5E2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...will be if<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-2x-x%5E2=0 ALIGN=MIDDLE  ALT=\"3-2x-x%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-3x%2Bx-x%5E2=0 ALIGN=MIDDLE  ALT=\"3-3x%2Bx-x%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%281-x%29%2Bx%281-x%29=0 ALIGN=MIDDLE  ALT=\"3%281-x%29%2Bx%281-x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2Bx%29%281-x%29=0 ALIGN=MIDDLE  ALT=\"%283%2Bx%29%281-x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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;\" >\r<BR>\n" );
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document.write( "domain is: { <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > element <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%3Cx%3C1 ALIGN=MIDDLE  ALT=\"-3%3Cx%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" > }\r<BR>\n" );
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document.write( "range:\r<BR>\n" );
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document.write( "to  find the range of a rational function use the derivative<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2Fdx%29%281%2Fsqrt%283+-+2+x+-+x%5E2%29%29+=+%28x+%2B+1%29%2F%28-x%5E2+-+2+x+%2B+3%29%5E%283%2F2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > => if numerator equal to zero then <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;\" >\r<BR>\n" );
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document.write( "plug in your function and find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   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=y=1%2F%28sqrt%283-2%28-1%29-%28-1%29%5E2%29%29=1%2Fsqrt%283%2B2-1%29=1%2Fsqrt%284%29=1%2F2 ALIGN=MIDDLE  ALT=\"y=1%2F%28sqrt%283-2%28-1%29-%28-1%29%5E2%29%29=1%2Fsqrt%283%2B2-1%29=1%2Fsqrt%284%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so range is { <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > element <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%3E=+1%2F2 ALIGN=MIDDLE  ALT=\"y+%3E=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > }\r<BR>\n" );
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document.write( "B): \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2F%28sqrt%28x%5E2%2B2x%2B3%29%29 ALIGN=MIDDLE  ALT=\"y=1%2F%28sqrt%28x%5E2%2B2x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> as you can see, no matter what  value is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, denominator cannot be equal to zero\r<BR>\n" );
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document.write( "domain: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > (all real numbers)\r<BR>\n" );
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document.write( "range:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2Fdx%29%281%2F%28sqrt%28x%5E2%2B2x%2B3%29%29%29=%28-x-1%29%2F%28x%5E2%2B2x%2B3%29%5E%283%2F2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > =>if numerator equal to zero then <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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2F%28sqrt%28%28-1%29%5E2%2B2%2A%28-1%29%2B3%29%29=1%2Fsqrt%281-2%2B3%29=1%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"y=1%2F%28sqrt%28%28-1%29%5E2%2B2%2A%28-1%29%2B3%29%29=1%2Fsqrt%281-2%2B3%29=1%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >->\r<BR>\n" );
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document.write( "so, range is: { <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > element <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0%3C+y+%3C=1%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"+0%3C+y+%3C=1%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > }\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );