document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=915027>Question 915027</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?\r<BR>\n" );
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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" );
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document.write( "I have looked at this for hours, but I just can't make sense of it.... Please explain and show work!\r<BR>\n" );
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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 #555402 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39616)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=555402\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have three choices.  Your composition equation given is to compose a function with itself.  Just test every choice I, II, and III, and see which one gives x as a result (when simplified).\r<BR>\n" );
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document.write( "What if you had a forth choice...<BR>\n" );
document.write( "IV.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-1%2Fx ALIGN=MIDDLE  ALT=\"f%28x%29=-1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Would this composed of itself be x?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28f%28x%29%29=-1%2F%28-1%2Fx%29 ALIGN=MIDDLE  ALT=\"f%28f%28x%29%29=-1%2F%28-1%2Fx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%281%2Fx%29=x ALIGN=MIDDLE  ALT=\"1%2F%281%2Fx%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I did not expect that, but this function is also its own inverse; meaning this function composed with itself will give back the input variable. </SPAN>\n" );
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