document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1028661>Question 1028661</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let f(x) = x^2 - 2x. Find all real numbers x such that f(x) = f(f(x)). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #643788 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=643788\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let y = f(x). We want to solve y = f(y).\r<BR>\n" );
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document.write( "Solving y = f(y) gives y = y^2 - 2y or y = 0, 3. Then we want to solve f(x) = 0, f(x) = 3.\r<BR>\n" );
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document.write( "If f(x) = 0, then x^2 - 2x = 0 --> x = 0 or 2.<BR>\n" );
document.write( "If f(x) = 3, then x^2 - 2x = 3 --> x = 3 or -1.\r<BR>\n" );
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document.write( "Solutions: 0, -1, 2, 3 </SPAN>\n" );
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