document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167698>Question 167698</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let r(x)=x^2-3 and s(x)=x^3-6.  Find r(s(-1)). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123607 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=123607\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28-1%29 ALIGN=MIDDLE  ALT=\"s%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the inner function)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28x%29=x%5E3-6 ALIGN=MIDDLE  ALT=\"s%28x%29=x%5E3-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the second function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28-1%29=%28-1%29%5E3-6 ALIGN=MIDDLE  ALT=\"s%28-1%29=%28-1%29%5E3-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <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=s%28-1%29=-1-6 ALIGN=MIDDLE  ALT=\"s%28-1%29=-1-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cube <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28-1%29=-7 ALIGN=MIDDLE  ALT=\"s%28-1%29=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract.\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28-1%29=-7 ALIGN=MIDDLE  ALT=\"s%28-1%29=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28s%28-1%29%29=r%28-7%29 ALIGN=MIDDLE  ALT=\"r%28s%28-1%29%29=r%28-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28-1%29 ALIGN=MIDDLE  ALT=\"s%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with -7)\r<BR>\n" );
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document.write( "So let's evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28-7%29 ALIGN=MIDDLE  ALT=\"r%28-7%29\"   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=r%28x%29=x%5E2-3 ALIGN=MIDDLE  ALT=\"r%28x%29=x%5E2-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28-7%29=%28-7%29%5E2-3 ALIGN=MIDDLE  ALT=\"r%28-7%29=%28-7%29%5E2-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7 ALIGN=MIDDLE  ALT=\"x=-7\"   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=r%28-7%29=49-3 ALIGN=MIDDLE  ALT=\"r%28-7%29=49-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49 ALIGN=MIDDLE  ALT=\"49\"   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=r%28-7%29=46 ALIGN=MIDDLE  ALT=\"r%28-7%29=46\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract.\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28-7%29=46 ALIGN=MIDDLE  ALT=\"r%28-7%29=46\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28s%28-1%29%29=46 ALIGN=MIDDLE  ALT=\"r%28s%28-1%29%29=46\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28s%28-1%29%29=46 ALIGN=MIDDLE  ALT=\"r%28s%28-1%29%29=46\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note: there is another way to do this which involves substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28x%29 ALIGN=MIDDLE  ALT=\"s%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28x%29 ALIGN=MIDDLE  ALT=\"r%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and evaluating the composite function at <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;\" >. However, this method is a bit more complicated. </SPAN>\n" );
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