document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1123452>Question 1123452</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I've been wrapping my head around this for a while and would like an easier explanation to solving these functions. Thank-you.\r<BR>\n" );
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document.write( "Suppose that the functions p and q are defined as follows.\r<BR>\n" );
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document.write( "p(x)= x^2+9<BR>\n" );
document.write( "q(x)= &#8730;x+8\r<BR>\n" );
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document.write( "Find:\r<BR>\n" );
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document.write( "(p &#8728; q)(8) = <BR>\n" );
document.write( "(q &#8728; p)(8) =  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #739785 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=739785\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Let's say you have a function <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x)\ =\ \frac{x^2\ +\ 1}{x\ -\ 5}\">\r<BR>\n" );
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document.write( "Then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(2)\ =\ \frac{(2)^2\ +\ 1}{2\ -\ 5}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(a)\ =\ \frac{a^2\ +\ 1}{a\ -\ 5}\">\r<BR>\n" );
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document.write( "as long as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\ \not=\ 5\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(TheArtistFormerlyKnownAsPrince)\ =\ \frac{(TheArtistFormerlyKnownAsPrince)^2\ +\ 1}{TheArtistFormerlyKnownAsPrince\ -\ 5\">\r<BR>\n" );
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document.write( "as long as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large TheArtistFormerlyKnownAsPrince\ \not=\ 5\">\r<BR>\n" );
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document.write( "The function <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (f\circ g)(x)\"> is EXACTLY the same thing as saying <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f\(g(x)\)\">.  In other words, take the definition of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x)\"> and every place you see an <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> put <i>the definition of</i> <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large g(x)\"> in its place.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (p\circ q)(x)\ =\ p\(q(x)\)\ =\ \(q(x)\)^2\ +\ 9\ =\ \(\sqrt{x}\ +\ 8\)^2\ +\ 9\ =\ x\ +\ 16\sqrt{x}\ +\ 64\ +\ 9\ =\ x\ +\ 16\sqrt{x}\ +\ 73\">\r<BR>\n" );
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document.write( "Then for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (p\circ q)(8)\"> just plug in 8 and do the arithmetic.  Hint:  For the exact answer is simplest form use <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt{8}\ =\ 2\sqrt{2}\">\r<BR>\n" );
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document.write( "Do the other one the same way.\r<BR>\n" );
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document.write( "By the way, this solution is incorrect if you actually meant <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large q(x)\ =\ \sqrt{x\ +\ 8}\"> instead of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large q(x)\ =\ \sqrt{x}\ +\ 8\">.  If this is the case, it is on you because you failed to put parentheses around the radicand in the definition of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large q\">.  My interpretation is correct based on what you wrote.<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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