document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=915234>Question 915234</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For which of the following functions is f(f(x)) = x, for all values of x in the domain of f? <BR>\n" );
document.write( "I. f(x) = x<BR>\n" );
document.write( "II. f(x) = -x<BR>\n" );
document.write( "III. f(x) = 1/x \r<BR>\n" );
document.write( "\n" );
document.write( "I have looked at this for hours, but I just can't make sense of it.... Please explain and show work! <BR>\n" );
document.write( "Your help is TRULY appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #555473 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=555473\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's try them out\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(x) = x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(f(x)) = f(x) ... replace EVERY x with f(x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(f(x)) = x ... replace f(x) on the right side with x (works because f(x) = x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so statement I is true.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "II.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(x) = -x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(f(x)) = -(f(x))\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(f(x)) = -(-x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(f(x)) = x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and II is also another answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "III. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(x) = 1/x \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(f(x)) = 1/(f(x))\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(f(x)) = 1/(1/x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(f(x)) = x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "========================================================================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "It turns out that all three functions f(x) = x, f(x) = -x and f(x) = 1/x make f(f(x)) = x true for all allowed inputs for x.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let me know if you need more help or if you need me to explain a step in more detail.<BR>\n" );
document.write( "Feel free to email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help\">jim_thompson5910@hotmail.com</a><BR>\n" );
document.write( "or you can visit my website here: <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">http://www.freewebs.com/jimthompson5910/home.html</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Thanks,\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Jim  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );