document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=905689>Question 905689</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Did I do this composite function correctly?\r<BR>\n" );
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document.write( "Let f(x) = 1/(2x), g(x) = 7x^3, and h(x) = &#8722;4x^2 + 1\r<BR>\n" );
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document.write( "(f º g º h)(x) = 1/(686(-4x^2+1)^3)\r<BR>\n" );
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document.write( "Is that right?<BR>\n" );
document.write( "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 #549369 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=549369\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i don't believe so.\r<BR>\n" );
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document.write( "i got something entirely different and i confirmed it is correct.\r<BR>\n" );
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document.write( "start with:\r<BR>\n" );
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document.write( "f(x) = 1/(2x)<BR>\n" );
document.write( "g(x) = 7x^3<BR>\n" );
document.write( "h(x) = -4x^2 + 1\r<BR>\n" );
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document.write( "(f.g.h)(x) = f(g(h(x)))\r<BR>\n" );
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document.write( "that translates to f of g of h of x.\r<BR>\n" );
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document.write( "you find h(x) first.<BR>\n" );
document.write( "then you find g(h(x)) next.<BR>\n" );
document.write( "then you find f(g(h(x))) next.\r<BR>\n" );
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document.write( "h(x) = (-4x^2 + 1)\r<BR>\n" );
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document.write( "g(h(x)) = g(-4x^2 + 1) = (7 * (-4x^2 + 1)^3)\r<BR>\n" );
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document.write( "f(g(h(x)) = f(7 * (-4x^2 + 1)^3) = 1 / (2 * (7 * (-4x^2 + 1)^3))\r<BR>\n" );
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document.write( "if you work it all through, you will get:\r<BR>\n" );
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document.write( "f(g(h(x)) = 1 / (-896x^6 + 672x^4 - 168x^2 + 2)\r<BR>\n" );
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document.write( "the piece parts are:\r<BR>\n" );
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document.write( "h(x) = -4x^2 + 1\r<BR>\n" );
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document.write( "g(h(x)) = -448x^6 + 336x^4 - 84x^2 + 1\r<BR>\n" );
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document.write( "f(g(h(x)) = 1 / (-896x^6 + 672x^4 - 168x^2 + 2)\r<BR>\n" );
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document.write( "i confirmed by assigning the arbitrary value of 7 to x and then solving from the original equations and then solving from the final equation.\r<BR>\n" );
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document.write( "i got:\r<BR>\n" );
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document.write( "h(7) = -195\r<BR>\n" );
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document.write( "g(-195) = -51904125\r<BR>\n" );
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document.write( "f(-51904125) = -9.63314573*10^-9\r<BR>\n" );
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document.write( "I then went to the final equation to get:\r<BR>\n" );
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document.write( "(f.g.h)(7) = f(g(h(7)) = -9.63314573*10^-9\r<BR>\n" );
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document.write( "since both answers are the same, i assume that i did it right.\r<BR>\n" );
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document.write( "you can find (-4x^2 + 1)^3 by first multiplying (-4x^2 + 1) by (-4x^2 + 1) and the multiplying the result by (-4x^2 + 1).\r<BR>\n" );
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document.write( "you can also find it by seeing that it is a binomial expansion of (a + b)^3 where a = -4x^2 and b = 1.\r<BR>\n" );
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document.write( "i did it both ways and got the same answer of (-4x^2 + 1)^3 = -64x^6 + 48x^4 - 12x^2 + 1\r<BR>\n" );
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document.write( " </SPAN>\n" );
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