document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=804336>Question 804336</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I understood everything until I got further on in the homework and now I do not get it! You do not have to solve the whole problem, I am very capable of doing that, but may you please at least help me set them up and explain them too so I can learn how to do it? Thank you so much!\r<BR>\n" );
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document.write( "Let f(x)=x^2 -1 and g(x)= 1- 2x. Find the indicated values for\r<BR>\n" );
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document.write( "A.  g(2g(1))<BR>\n" );
document.write( "B.  g(1/f(3))<BR>\n" );
document.write( "C.  g(a+1)-g(a)<BR>\n" );
document.write( "D.  f(a+1)-f(a)<BR>\n" );
document.write( "E.  f(x+h) - f(x)/h\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #484711 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=484711\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\"><BR>\n" );
document.write( "The one thing you have to remember is that given some <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x)\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(1)\"> is the same thing with <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> replaced by 1.  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(a)\"> is the same thing with <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> replaced by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a\">.  So if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x)\ =\ x^2\ -\ 3x\ +\ 2\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(2)\ =\ (2)^2\ -\ 3(2)\ +\ 2\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(a)\ =\ a^2\ -\ 3a\ +\ 2\">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(gobbledegook)\ =\ (gobbledegook)^2\ -\ 3(gobbledegook)\ +\ 2\">\r<BR>\n" );
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document.write( "For part A, start by evaluating g(1).  Then multiply that value by 2.  Then evalute g at that value.  g(1) is 1 - 2(1) = -1. 2 times -1 is -2.  Then g(-2) is 1 - 2(-2) = 1 - (-4) = 5.\r<BR>\n" );
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document.write( "Now, let's do part E.\r<BR>\n" );
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document.write( "Given <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x)\ =\ x^2\ -\ 1\">, evaluate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{f(x\ +\ h)\ -\ f(x)}{h}\">\r<BR>\n" );
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document.write( "Start by defining <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE f(x\ +\ h) =\ (x\ +\ h)^2\ -\ 1\">\r<BR>\n" );
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document.write( "Now plug in everything you know:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{(x\ +\ h)^2\ -\ 1\ -\ (x^2\ -\ 1)}{h}\">\r<BR>\n" );
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document.write( "Now all you have to do is expand the binomial and collect like terms.  If you are careful about your signs, all of the terms you have left after collecting like terms will have at least one factor of h.  You can then divide through by h, getting that pesky thing out of your denominator -- always the goal when working out a difference quotient.\r<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( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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