document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=4808>Question 4808</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please give me the proper equation for (f o g)(3) given f(x) = 11x + 5 and g(x) = x2 + 8x?\r<BR>\n" );
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document.write( "Also, (g o f)(2), Given f(x) = 2x + 9 and g(x) = x2 + 7x.\r<BR>\n" );
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document.write( "Please keep in mind I have a math learning disability, so the simpler the explanation, the better I'll understand it.  I'm 46 and if I don't pass this class, I don't graduate in May. :)  Thanks for your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #2310 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=2310\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (f o g)(3) given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+11x+%2B+5 ALIGN=MIDDLE  ALT=\"f%28x%29+=+11x+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29+=+x%5E2+%2B+8x ALIGN=MIDDLE  ALT=\"g%28x%29+=+x%5E2+%2B+8x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(f o g)(3) means f[ g(3) ], so the first order of business is to find g(3).  Go to the g(x) formula and substitute 3 for the x, giving you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2+%2B+8%2A+3 ALIGN=MIDDLE  ALT=\"3%5E2+%2B+8%2A+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "g(3) = 9 + 24 = 33\r<BR>\n" );
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document.write( "Now, find f[ g(3) ] = f[ 33 ] = 11*33 + 5 = 3685  \r<BR>\n" );
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document.write( "Second problem (g o f)(2), Given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2x+%2B+9+ ALIGN=MIDDLE  ALT=\"f%28x%29+=+2x+%2B+9+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29+=+x%5E2+%2B+7x ALIGN=MIDDLE  ALT=\"g%28x%29+=+x%5E2+%2B+7x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "(g o f)(2) means g[ f(2) ], so you first have to find f(2) using the f(x) formula.<BR>\n" );
document.write( "f(2) = 2*2 + 9 = 13\r<BR>\n" );
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document.write( "Now you have to find g(13) using the g(x) formula:<BR>\n" );
document.write( "(g o f)(2) = g[ f(2) ] = g[ 13 ] = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%5E2+%2B+7%2A+13 ALIGN=MIDDLE  ALT=\"13%5E2+%2B+7%2A+13\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 169 + 91 = 260\r<BR>\n" );
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document.write( "There really isn't a good way to check these without going to twice as much work as solving them to begin with.  Such ugly answers!  Sorry about that.  \r<BR>\n" );
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document.write( "R^2 at SCC<BR>\n" );
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