document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140385>Question 1140385</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please explain:\r<BR>\n" );
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document.write( "If f(x)=4/x    and g(x)=3x^5, find (g ∘ f)(x)\r<BR>\n" );
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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 #760901 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=760901\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = 4/x<BR>\n" );
document.write( "g(x) = 3x^5\r<BR>\n" );
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document.write( "(g ∘ f)(x) is the same as g(f(x)).\r<BR>\n" );
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document.write( "that's pronounced g of f(x).\r<BR>\n" );
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document.write( "here's how it works.\r<BR>\n" );
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document.write( "f(x) = 4/x\r<BR>\n" );
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document.write( "g(x) = 3x^5\r<BR>\n" );
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document.write( "g(f(x)) is equal to g(4/x) which becomes 3 * (4/x) ^ 5\r<BR>\n" );
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document.write( "you are replacing the x in g(x) with f(x) which is equal to 4/x.\r<BR>\n" );
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document.write( "the result is g(f(x)) = g(4/x) = 3 * (4/x) ^ 5 = 3 * 4^5 / x^5 = 3072 / x^5.\r<BR>\n" );
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document.write( "the best way to see how this works is to let x = some random number that's not too big or to small that it becomes unwieldy.\r<BR>\n" );
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document.write( "i chose x = 2 because it gives you a clean answer.\r<BR>\n" );
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document.write( "you have f(x) = 4/x which becomes f(x) = 4/2 which becomes f(x) = 2.\r<BR>\n" );
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document.write( "that's f(x).\r<BR>\n" );
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document.write( "g(x) = 3 * x ^ 5\r<BR>\n" );
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document.write( "you replace x in g(x) with f(x)) which is equal to 2.\r<BR>\n" );
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document.write( "g(f(x)) becomes g(2) which becomes 3 * 2 ^ 5 which becomes 96.\r<BR>\n" );
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document.write( "now we previously solved for g(f(x)) in terms of x.\r<BR>\n" );
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document.write( "that became g(f(x)) = 3 * (4 / x) ^ 5 which becomes 3072 / x^5.\r<BR>\n" );
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document.write( "when x = 2, we get g(f(x)) = 3072 / x^5 which becomes 3072 / 2^5 which becomes 3072 / 32 which becomes 96.\r<BR>\n" );
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document.write( "here's a pretty complete reference on composition of functions that you might find informative.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.purplemath.com/modules/fcncomp.htm\" target = \"_blank\">https://www.purplemath.com/modules/fcncomp.htm</a>\r<BR>\n" );
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document.write( "if any part of it confuses you, let me know and i'll explain as best i can.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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