document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1091007>Question 1091007</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let f(x)=x+2 and g(x)=x/3. Also denote the inverses to these functions as f^{-1} and g^{-1}. Compute f(g^{-1}(f^{-1}(f^{-1}(g(f(19)))))). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #705465 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=705465\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>There is nothing complicated about this except the notation.  You just need to make sure you start with the innermost parentheses -- which means you work from right to left to evaluate the given expression.<br><BR>\n" );
document.write( "As for the notation, let me use F and G for the inverses of the two given functions.<br><BR>\n" );
document.write( "And of course you need to know that<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%2B2 ALIGN=MIDDLE  ALT=\"f%28x%29=x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%28x%29=x-2 ALIGN=MIDDLE  ALT=\"F%28x%29=x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=x%2F3 ALIGN=MIDDLE  ALT=\"g%28x%29=x%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=G%28x%29=3x ALIGN=MIDDLE  ALT=\"G%28x%29=3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%2819%29=21 ALIGN=MIDDLE  ALT=\"f%2819%29=21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%2821%29=7 ALIGN=MIDDLE  ALT=\"g%2821%29=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%287%29=5 ALIGN=MIDDLE  ALT=\"F%287%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=F%285%29=3 ALIGN=MIDDLE  ALT=\"F%285%29=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%283%29=9 ALIGN=MIDDLE  ALT=\"G%283%29=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%289%29=11 ALIGN=MIDDLE  ALT=\"f%289%29=11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );