document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=969381>Question 969381</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with this problem\r<BR>\n" );
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document.write( "Let f=(&#8722;1&#719;2)&#719;(0&#719;&#8722;2)g=(&#8722;1&#719;&#8722;3)&#719;(4&#719;1)&#719;(&#8722;4&#719;&#8722;3) <BR>\n" );
document.write( "Find f+g and its domain </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592323 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=592323\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a good reference for what you are asking is here.<BR>\n" );
document.write( "it took a while to find it, but i was able to get what i was looking for.<BR>\n" );
document.write( "not all references talk about operations on functions when you are given sets of point pairs.<BR>\n" );
document.write( "this one does.<BR>\n" );
document.write( "good thing too because it clears up a very basic assumption regarding what's defined and what's not defined and whether you can add two functions together when one of the x values is defined and the other x value is not defined, as is the case with your problem.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut30b_operations.htm\" target = \"_blank\">http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut30b_operations.htm</a><BR>\n" );
document.write( "based on this reference, there is only one point pair that is in both sets.<BR>\n" );
document.write( "that would be the point pair of (-1,2) in f and the point pair of (-1,-3) in g.<BR>\n" );
document.write( "f+g would therefore be f(-1) + g(-1) which is equal to 2 - 3 which is equal to -1.<BR>\n" );
document.write( "the point pair in f+g is therefore (-1,-1).<BR>\n" );
document.write( "it's the only point pair that's in both functions and therefore the only point pair that is valid.<BR>\n" );
document.write( "the domain of f+g is -1 only because the x value of -1 is the only x value that's in both sets.<BR>\n" );
document.write( "read the reference and you'll see what i mean.<BR>\n" );
document.write( "it's an excellent reference on the topic and you are well advised to read it and understand it.<BR>\n" );
document.write( "in relation to your problem, the intersection of the sets is (-1) only and so your only domain in f+g is at x = -1 where you get f+g(-1) = -1 which results in the point pair of (-1,-1).\r<BR>\n" );
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