document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=82614>Question 82614</A>: <I><SPAN STYLE=\"word-break: break-all;\"> re-writing my previous question, format didn't come out the way it was supposed to look like: \r<BR>\n" );
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document.write( "a) show that if f is any function, then the function E defined by: <BR>\n" );
document.write( "E(x)= [(f(x)+f(-x))/2]is even\r<BR>\n" );
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document.write( "b) show that if f is any function, then the function O defined by \r<BR>\n" );
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document.write( "O(x)= [(f(x)-f(-x))/2] is odd   \r<BR>\n" );
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document.write( "i hope the parenthetical notation is correct.  basically, the functions E(x) and O(x) have f(x)adding or subtracting f(-x) and the sum or difference is then divided by 2.\r<BR>\n" );
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document.write( "thanks, sorry about the confusion, the first time i posted i tried to get fancy with the formatting, it didn't work i hope this one makes sense </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59225 by </B><A HREF=/tutors/aboutme.mpl?userid=kev82><B>kev82(151)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kev82><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=59225\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi,<br />\r<BR>\n" );
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document.write( "This is simply a case of using one of the definitions of even and odd. A function E(x) is even if E(-x)=E(x), and a function O(x) is odd if O(-x)=-O(x).<br />\r<BR>\n" );
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document.write( "I'll do the even one, hopefully you can do the odd one on your own.<br />\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?E(-x)=\frac{f(-x)+f(x)}{2}=\frac{f(x)+f(-x)}{2}=E(x)\"><br />\r<BR>\n" );
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document.write( "See if you can do the same thing for the odd one.<br />\r<BR>\n" );
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document.write( "Hope that helps,<BR>\n" );
document.write( "Kev </SPAN>\n" );
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