document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012362>Question 1012362</A>: <I><SPAN STYLE=\"word-break: break-all;\"> gog=g(g(x)) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #628265 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=628265\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> gog(x) = g(g(x)).\r<BR>\n" );
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document.write( "this is no different than fog(x) = f(g(x)), when the function called f is the exact same function as the function called g.\r<BR>\n" );
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document.write( "here's an example of gog(x).\r<BR>\n" );
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document.write( "let g(x) = x^2\r<BR>\n" );
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document.write( "gog(x) = g(g(x))\r<BR>\n" );
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document.write( "since g(x) = x^2, g(g(x)) becomes g(x^2).\r<BR>\n" );
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document.write( "since g(x) = x^2, then g(x^2) = (x^2)^2 = x^4.\r<BR>\n" );
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document.write( "when the argument is x, g(x) = x^2\r<BR>\n" );
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document.write( "when the argument is x^2 rather than x, you raplace x with x^2 to get g(x^2) = (x^2)^2.\r<BR>\n" );
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document.write( "let's do it with numbers to see if that's any clearer.\r<BR>\n" );
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document.write( "g(x) = x^2\r<BR>\n" );
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document.write( "let's find g(2).\r<BR>\n" );
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document.write( "g(2) = 2^2 = 4\r<BR>\n" );
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document.write( "gog(2) = g(g(2))\r<BR>\n" );
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document.write( "since g(2) = 4, then g(g(2)) = g(4) = 4^2 = 16.\r<BR>\n" );
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document.write( "the result from the inner function is passed to the outer function and then the outer function works on that.\r<BR>\n" );
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document.write( "bottom line:\r<BR>\n" );
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document.write( "gog(x) is the same as fog(x) when f performs the exact same function as g.\r<BR>\n" );
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document.write( "if f(x) = x^2 and g(x) = x^2, you would get exactly the same result from fog(x) as you would get from gog(x).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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