document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=32436>Question 32436</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear tutors, \r<BR>\n" );
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document.write( "Please explain how to solve these kind of functions.  \r<BR>\n" );
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document.write( "For which of the following functions f is f(x) = f(1-x) for all x.\r<BR>\n" );
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document.write( "a.	f(x) = 1-x<BR>\n" );
document.write( "b.	f(x) = 1-x^2 (x squared)<BR>\n" );
document.write( "c.	f(x) = x^2 – (1-x)^2<BR>\n" );
document.write( "d.	f(x) = x^2(1-x)^2<BR>\n" );
document.write( "e.	f(x) = x/( 1-x)\r<BR>\n" );
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document.write( "by the way, this question is from a paper test i bought online.  \r<BR>\n" );
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document.write( "Regards, <BR>\n" );
document.write( "Tolly </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #18934 by </B><A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><B>mukhopadhyay(490)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><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=18934\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = f(1-x) for all x<BR>\n" );
document.write( "......................<BR>\n" );
document.write( "a. f(x) = 1-x<BR>\n" );
document.write( "=> f(1-x) = 1-(1-x) = x<BR>\n" );
document.write( "f(x)=f(1-x) => x=1-x => x=1/2;<BR>\n" );
document.write( "............<BR>\n" );
document.write( "b. f(x) = 1-x^2 <BR>\n" );
document.write( "=> 1-x^2 = x^2 (using the same approach as above)<BR>\n" );
document.write( "=> x^2 = 1/2 => x=1/sqrt(2) or x=-1/(sqrt(2);<BR>\n" );
document.write( ".........................<BR>\n" );
document.write( "c. f(x) = x^2 – (1-x)^2<BR>\n" );
document.write( "=> x^2 - (1-x)^2 = (1-x)^2 - (x^2)  (using the same approach as in a.)<BR>\n" );
document.write( "=> x^2 = (1-x)^2<BR>\n" );
document.write( "=> (x)(x) = 0<BR>\n" );
document.write( "=> x=0<BR>\n" );
document.write( "........................<BR>\n" );
document.write( "d. f(x) = x^2(1-x)^2<BR>\n" );
document.write( "=> x^2(1-x)^2 = (1-x)^2(x^2)   (using the same approach as in a.)<BR>\n" );
document.write( "The above is true for all real x => x is any real number<BR>\n" );
document.write( ".............<BR>\n" );
document.write( "e. f(x) = x/( 1-x) <BR>\n" );
document.write( "=> x/(1-x) = (1-x)/x   (using the same approach as in a.)<BR>\n" );
document.write( "=> x^2 = (1-x)^2<BR>\n" );
document.write( "=> x^2 = x^2-2x+1<BR>\n" );
document.write( "=> x = 1/2<BR>\n" );
document.write( " </SPAN>\n" );
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