document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191148>Question 1191148</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given f(x) =-6x^2-8x<BR>\n" );
document.write( "I) (f°f)(1)<BR>\n" );
document.write( "Given g(x)= -12x-5<BR>\n" );
document.write( "Find g^-1(5)<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 #822912 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=822912\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> problem 1:\r<BR>\n" );
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document.write( "Given f(x) =-6x^2-8x, find f(f(1))\r<BR>\n" );
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document.write( "f(x) = -6x^2 - 8x<BR>\n" );
document.write( "when x = 1, f(1) = -6 -8 = -14.\r<BR>\n" );
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document.write( "f(f(x)) = -6 * (-6x^2-8x)^2 - 8 * (-6x^2-8x)<BR>\n" );
document.write( "when x = 1, -6x^2-8x = -14, therefore:<BR>\n" );
document.write( "-f(f(1)) = -6 * (-14)^2 - 8 * -14 = -1064.\r<BR>\n" );
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document.write( "your solution is that f(f(1) = -1064.\r<BR>\n" );
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document.write( "this can be graphed.<BR>\n" );
document.write( "the graph shows that the value of f(1) = -14 and the value of f(f(1)) = -1064.<BR>\n" );
document.write( "here's the graph.<BR>\n" );
document.write( "f(x) is in red.<BR>\n" );
document.write( "f(f(x) is in blue\r<BR>\n" );
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document.write( "problem 2:\r<BR>\n" );
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document.write( "Given g(x)= -12x-5, find g^-1(5)\r<BR>\n" );
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document.write( "g^-1(x) is the inverse of g(x).<BR>\n" );
document.write( "to find it, replace g(x) with y and then replace y with x and x with y and then solve for y.<BR>\n" );
document.write( "start with:<BR>\n" );
document.write( "g(x) = -12x-5<BR>\n" );
document.write( "replace g(x) with y to get:<BR>\n" );
document.write( "y = -12x-5<BR>\n" );
document.write( "replace y with x and x with y to get:<BR>\n" );
document.write( "x = -12y-5<BR>\n" );
document.write( "switch sides to get:<BR>\n" );
document.write( "-12y-5 = x<BR>\n" );
document.write( "add 5 to both sides to get:<BR>\n" );
document.write( "-12y = x+5<BR>\n" );
document.write( "divide both sides by -12 to get:<BR>\n" );
document.write( "y = -(x+5)/12<BR>\n" );
document.write( "replace y with g^-1(x) to get:<BR>\n" );
document.write( "g^-1(x) = -(x+5)/12\r<BR>\n" );
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document.write( "when x = 5, .....\r<BR>\n" );
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document.write( "g(x) = -12x-5 becomes -12 * 5 - 5 = -65<BR>\n" );
document.write( "g^-1(x) = -(x+5)/12 = -10/12 = -.8333\r<BR>\n" );
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document.write( "g(x) and g^-1(x) can be graphed.<BR>\n" );
document.write( "the graph is shown below.<BR>\n" );
document.write( "in the graph, g(x) is replaced with y and g^-1(x) is replaced with y.<BR>\n" );
document.write( "g(x) is in red.<BR>\n" );
document.write( "g^-1(x) is in blue.\r<BR>\n" );
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document.write( "let me know if you have any questions or concerns.<BR>\n" );
document.write( "theo\r<BR>\n" );
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