document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1034616>Question 1034616</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the rules for the composite functions (g &#9702; f)(x) and (f &#9702; g)(x) <BR>\n" );
document.write( "b) If f(x) = 4 &#8722; 4x + x^2 and g(x) = x^2/x &#8722; 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #649270 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=649270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-4x%2Bx%5E2%29 ALIGN=MIDDLE  ALT=\"%284-4x%2Bx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "g(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2F%28x-4%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2F%28x-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "fog(x) = f(g(x))\r<BR>\n" );
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document.write( "gof(x) = g(f(x))\r<BR>\n" );
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document.write( "i use the letter \"o\" to indicate the composition symbol.<BR>\n" );
document.write( "it's easier than trying to figure out what the code for the composition symbol is.\r<BR>\n" );
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document.write( "the argument in f(x) is equal to x.<BR>\n" );
document.write( "the argument in f(g(x)) is equal to g(x).<BR>\n" );
document.write( "in order to find fog(x), you need to replace the argument of x with the argument of g(x).<BR>\n" );
document.write( "since g(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2F%28x-4%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2F%28x-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you need to replace x in f(x) with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2F%28x-4%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2F%28x-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "you will get:\r<BR>\n" );
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document.write( "f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-4x%2Bx%5E2%29 ALIGN=MIDDLE  ALT=\"%284-4x%2Bx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "f(g(x)) =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-4%2Ag%28x%29%2Bg%28x%29%5E2%29 ALIGN=MIDDLE  ALT=\"%284-4%2Ag%28x%29%2Bg%28x%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since g(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2F%28x-4%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2F%28x-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then .....\r<BR>\n" );
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document.write( "f(g(x)) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-4%2A%28x%5E2%2F%28x-4%29%29%2B%28x%5E2%2F%28x-4%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"%284-4%2A%28x%5E2%2F%28x-4%29%29%2B%28x%5E2%2F%28x-4%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "likewise, .....<BR>\n" );
document.write( "the argument in g(x) is x.<BR>\n" );
document.write( "the argument in g(f(x)) is f(x).<BR>\n" );
document.write( "in order to find gof(x), you need to replace the argument of x with the argument of f(x).<BR>\n" );
document.write( "since f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-4x%2Bx%5E2%29 ALIGN=MIDDLE  ALT=\"%284-4x%2Bx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you need to replace x in g(x) with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-4x%2Bx%5E2%29 ALIGN=MIDDLE  ALT=\"%284-4x%2Bx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "you will get:\r<BR>\n" );
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document.write( "g(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2F%28x-4%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2F%28x-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "g(f(x)) =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28f%28x%29%5E2%2F%28f%28x%29-4%29%29 ALIGN=MIDDLE  ALT=\"%28f%28x%29%5E2%2F%28f%28x%29-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since f(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-4x%2Bx%5E2%29 ALIGN=MIDDLE  ALT=\"%284-4x%2Bx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then .....\r<BR>\n" );
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document.write( "g(f(x)) =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284-4x%2Bx%5E2%29%5E2%2F%28%284-4x%2Bx%5E2%29-4%29%29 ALIGN=MIDDLE  ALT=\"%28%284-4x%2Bx%5E2%29%5E2%2F%28%284-4x%2Bx%5E2%29-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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