document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=984759>Question 984759</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let f(x)=2x+3 and g(x)=x^2 \r<BR>\n" );
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document.write( "Determine the formula for the following composition:\r<BR>\n" );
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document.write( "(g o g o g...o g)(x) where there are n copies of the function g\r<BR>\n" );
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document.write( "This is a complete mystery o me, not even sure where to start. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #605564 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=605564\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Look for how you can deduce the pattern. <BR>\n" );
document.write( "Start with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=2 ALIGN=MIDDLE  ALT=\"n=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29og%28x%29=%28x%5E2%29%5E2=x%5E4 ALIGN=MIDDLE  ALT=\"g%28x%29og%28x%29=%28x%5E2%29%5E2=x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=3 ALIGN=MIDDLE  ALT=\"n=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29og%28x%29og%28x%29=%28x%5E2%29%5E4=x%5E8 ALIGN=MIDDLE  ALT=\"g%28x%29og%28x%29og%28x%29=%28x%5E2%29%5E4=x%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=4 ALIGN=MIDDLE  ALT=\"n=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29og%28x%29og%28x%29og%28x%29=%28x%5E2%29%5E8=x%5E16 ALIGN=MIDDLE  ALT=\"g%28x%29og%28x%29og%28x%29og%28x%29=%28x%5E2%29%5E8=x%5E16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the exponent is increasing as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5En ALIGN=MIDDLE  ALT=\"2%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > copies,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=G%5Bn%5D%28x%29=x%5E%282%5En%29 ALIGN=MIDDLE  ALT=\"G%5Bn%5D%28x%29=x%5E%282%5En%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where <BR>\n" );
document.write( "G[n]=g(x) o g(x) o g(x) ... g(x) <--- n times </SPAN>\n" );
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