document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=86977>Question 86977</A>: <I><SPAN STYLE=\"word-break: break-all;\">     Let f(x) be any function and O(x) = [f(x) – f(-x)]/2 .  Show that O(x) is odd. This question is really giving me a hard time. I would love it if someone could please help me. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #62941 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=62941\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let f(x) be any function and O(x) = [f(x) – f(-x)]/2 .  Show that O(x) is odd.<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "Condition to be \"odd\": O(x) has to equal -O(-x)<BR>\n" );
document.write( "O(x) = [f(x) – f(-x)]/2<BR>\n" );
document.write( "-O(-x) = -[f(-x)-f(--x)]/2<BR>\n" );
document.write( "= -[f(-x)-f(x)]/2<BR>\n" );
document.write( "=  [f(x)-f(-x)]/2<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "Since the required \"condition\" is met, O(x) is odd.<BR>\n" );
document.write( "================<BR>\n" );
document.write( "cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );