document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1020946>Question 1020946</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi there\r<BR>\n" );
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document.write( "My question is: For each pair of functions, obtain a formula for f(g(x)) and also for g(f(x))\r<BR>\n" );
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document.write( "f(x)=2x+3<BR>\n" );
document.write( "g(x)=3x+2\r<BR>\n" );
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document.write( "Can you show ALL your working to perhaps help me to understand better - would be very much appreciated<BR>\n" );
document.write( "Thanks so much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #636745 by </B><A HREF=/tutors/aboutme.mpl?userid=FrankM><B>FrankM(1040)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=FrankM><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=FrankM><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=636745\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am going to borrow a strategy from the Calculus for dummies author - \r<BR>\n" );
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document.write( "For  f(g(x)) think of \r<BR>\n" );
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document.write( "f(x)=2x+3 as f(stuff)=2(stuff)+3 in other words, the f(stuff ) function says to take that stuff, double it and add 3.\r<BR>\n" );
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document.write( "but here, stuff=g(x)=3x+2\r<BR>\n" );
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document.write( "so f(stuff)=2(stuff)+3 just needs the substitution, stuff=3x+2 and \r<BR>\n" );
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document.write( "f(g(x))=2(3x+2)+3 = 6x+7\r<BR>\n" );
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document.write( "Now, let's check real quick with one substitution X=1.\r<BR>\n" );
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document.write( "f(x)=2x+3<BR>\n" );
document.write( "g(x)=3x+2 \r<BR>\n" );
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document.write( "g(1)=3(1)+2=5<BR>\n" );
document.write( "f(5)=2(5)+3=13\r<BR>\n" );
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document.write( "f(g(1))=6x+7= 13  (check)\r<BR>\n" );
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document.write( "Now the next one needs less explaining.\r<BR>\n" );
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document.write( " g(f(x))\r<BR>\n" );
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document.write( "g(f(x))=3(2x+3)+2= 6x+11  << don't forget to check. \r<BR>\n" );
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document.write( " </SPAN>\n" );
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