document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205886>Question 1205886</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the pair of functions to find  f(g(x))<BR>\n" );
document.write( "  and  g(f(x))<BR>\n" );
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document.write( "f(x)=sqrt(x)+8,g(x)=x^2+3\r<BR>\n" );
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document.write( "f(g(x))=\r<BR>\n" );
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document.write( "g(f(x))= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842967 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=842967\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = sqrt(x) + 8<BR>\n" );
document.write( "g(x) = x^2 + 3\r<BR>\n" );
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document.write( "to find f(g(x)), replace x in f(x) with g(x) to get:<BR>\n" );
document.write( "f(g(x)) = sqrt(g(x)) + 8<BR>\n" );
document.write( "since g(x) = x^2 + 3, you get:<BR>\n" );
document.write( "f(g(x)) = sqrt(x^2 + 3) + 8\r<BR>\n" );
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document.write( "when x = 3, you get:<BR>\n" );
document.write( "f(g(x)) = sqrt(3^2 + 3) + 8 = 11.46410162\r<BR>\n" );
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document.write( "this is equivalent to finding g(x) first and then finding f(g(x)).<BR>\n" );
document.write( "g(x) = x^2 + 3.<BR>\n" );
document.write( "when x = 3, g(x) = 3^2 + 3 = 12.<BR>\n" );
document.write( "f(g(x)) becomes f(12) = sqrt(12) + 8 = 11.46410162.\r<BR>\n" );
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document.write( "f(x) and g(x) are repeated here to make them easier to reference.\r<BR>\n" );
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document.write( "f(x) = sqrt(x) + 8<BR>\n" );
document.write( "g(x) = x^2 + 3\r<BR>\n" );
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document.write( "to find g(f(x)), replace x in g(x) with f(x) to get:<BR>\n" );
document.write( "g(f(x)) = f(x)^2 + 3<BR>\n" );
document.write( "since f(x) = sqrt(x) + 8, you get:<BR>\n" );
document.write( "g(f(x)) = (sqrt(x) + 8)^2 + 3\r<BR>\n" );
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document.write( "when x = 3, you get:<BR>\n" );
document.write( "g(f(x)) = (sqrt(3) + 8)^2 + 3 = 97.71281292.\r<BR>\n" );
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document.write( "this is equivalent to finding f(x) first and then finding g(f(x)).<BR>\n" );
document.write( "f(x) = sqrt(x) + 8<BR>\n" );
document.write( "when x = 3, f(x) = sqrt(3) + 8 = 9.732050808.<BR>\n" );
document.write( "g(f(x)) becomes g(9.732050808) = 9.732050808^2 + 3 = 97.71281292.\r<BR>\n" );
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document.write( "your solution is:\r<BR>\n" );
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document.write( "f(g(x)) = sqrt(x^2 + 3) + 8\r<BR>\n" );
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document.write( "g(f(x)) = (sqrt(x) + 8)^2 + 3\r<BR>\n" );
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document.write( "here's a reference on composite functions.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.youtube.com/watch?v=QXGQtkbyFTs\" target = \"_blank\">https://www.youtube.com/watch?v=QXGQtkbyFTs</a>\r<BR>\n" );
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document.write( "there are more videos on youtube regarding composition of functions, so feel free to look for others if looking at one is insufficient.<BR>\n" );
document.write( "this particular tutor is pretty good as far as i can tell.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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