document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=896678>Question 896678</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the composition function f(g(x))\r<BR>\n" );
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document.write( "f(u)=3u^2+3u-4 and g(x)=x+1\r<BR>\n" );
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document.write( "f(g(x)) =?\r<BR>\n" );
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document.write( "Please help I keep getting it wrong. Not sure what I am doing wrong since I substitute \"x+1\" for every \"u\" and distribute. Any help will be greatly appreciated and thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #543700 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=543700\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> that's what you should be doing as far as i can see.<BR>\n" );
document.write( "let me see what i can get and we can compare notes.\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "g(x) = x + 1\r<BR>\n" );
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document.write( "f(u) = 3u^2 + 3u - 4\r<BR>\n" );
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document.write( "to find f(g(x)), you replace u with x+1 and evaluate.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "f(g(x)) = 3(x+1)^2 + 3(x+1) - 4 which becomes:\r<BR>\n" );
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document.write( "f(g(x)) = 3(x^2 + 2x + 1) + 3x + 3 - 4 which becomes:\r<BR>\n" );
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document.write( "f(g(x)) = 3x^2 + 6x + 3 + 3x + 3 - 4\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "f(g(x)) = 3x^2 + 9x + 2\r<BR>\n" );
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document.write( "that's your solution.\r<BR>\n" );
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document.write( "an easy way to check it out is as follows:\r<BR>\n" );
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document.write( "let x = 3 (any value of x chosen at random will do)\r<BR>\n" );
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document.write( "g(x) = 3+1 = 4\r<BR>\n" );
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document.write( "f(4) = 3*4^2 + 3*4 - 4 = 48 + 12 - 4 = 56\r<BR>\n" );
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document.write( "now go to your final equation and solve using x = 3\r<BR>\n" );
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document.write( "f(g(x)) = 3x^2 + 9x + 2 becomes:\r<BR>\n" );
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document.write( "f(g(3)) = 3*3^2 + 9*3 + 2 which becomes:\r<BR>\n" );
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document.write( "f(g(3)) = 3*9 + 27 + 2 which becomes:\r<BR>\n" );
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document.write( "f(g(3)) = 27 + 27 + 2 which becomes:\r<BR>\n" );
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document.write( "f(g(3)) = 56\r<BR>\n" );
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document.write( "both the original equations and the final equations give you the same answer so you're good.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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