document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1162538>Question 1162538</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this question. Thank you!<BR>\n" );
document.write( "a) Given the functions f(x) = x + 2 and g(x) = 3^x, determine an equation for (f ∘ g)(x) and (g ∘ f)(x).<BR>\n" );
document.write( "b) Determine f(g(3)) and g(f(3)). <BR>\n" );
document.write( "c) Determine all values of x for which f(g(x)) = g(f(x)). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #786350 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=786350\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x+%2B+2+ ALIGN=MIDDLE  ALT=\"f%28x%29+=+x+%2B+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29+=+3%5Ex ALIGN=MIDDLE  ALT=\"g%28x%29+=+3%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "determine an equation for: \r<BR>\n" );
document.write( "\n" );
document.write( "a.\r<BR>\n" );
document.write( "\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" > ∘ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g ALIGN=MIDDLE  ALT=\"g\"   DISABLED_style= \"max-width:90%; height:auto;\" >)(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >) =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29=f%283%5Ex%29=3%5Ex%2B2 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29=f%283%5Ex%29=3%5Ex%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "and <BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g+ ALIGN=MIDDLE  ALT=\"g+\"   DISABLED_style= \"max-width:90%; height:auto;\" >∘ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >)(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28f%28x%29%29=g%28x%2B2%29=3%5E%28x%2B2%29 ALIGN=MIDDLE  ALT=\"g%28f%28x%29%29=g%28x%2B2%29=3%5E%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "b. Determine <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%283%29%29 ALIGN=MIDDLE  ALT=\"f%28g%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28f%283%29%29 ALIGN=MIDDLE  ALT=\"g%28f%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
document.write( "\n" );
document.write( "first <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%283%29+=+3%5E3=27 ALIGN=MIDDLE  ALT=\"g%283%29+=+3%5E3=27\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%283%29%29=x%2B2=27%2B2=29 ALIGN=MIDDLE  ALT=\"f%28g%283%29%29=x%2B2=27%2B2=29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29+=+x+%2B+2=3%2B2=5+ ALIGN=MIDDLE  ALT=\"f%283%29+=+x+%2B+2=3%2B2=5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28f%283%29%29=3%5Ex=3%5E5=243 ALIGN=MIDDLE  ALT=\"g%28f%283%29%29=3%5Ex=3%5E5=243\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c) Determine all values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > for which <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28g%28x%29%29+=+g%28f%28x%29%29 ALIGN=MIDDLE  ALT=\"f%28g%28x%29%29+=+g%28f%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2=3%5Ex ALIGN=MIDDLE  ALT=\"x%2B2=3%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >....evidently, one solution is <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" );
document.write( "\n" );
document.write( "verify:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B2=3%5E1 ALIGN=MIDDLE  ALT=\"1%2B2=3%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=3 ALIGN=MIDDLE  ALT=\"3=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >->true\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );