document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=39601>Question 39601</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please explain to me how this equation can be a function\r<BR>\n" );
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document.write( "x^2=1+y^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #25040 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=25040\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Please explain to me how this equation can be a function<BR>\n" );
document.write( "x^2=1+y^2<BR>\n" );
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document.write( "PLEASE FIND BELOW EXPLANATION ON FUNCTION,RELATION AND<BR>\n" );
document.write( "FUNCTION OF A FUNCTION..FROM GENERAL ENGLISH AND<BR>\n" );
document.write( "MATHHEMATICALLY SPEAKING.<BR>\n" );
document.write( "NOW COMING TO F O G IN ENGLISH.LET ME TRY..<BR>\n" );
document.write( "FISTLY IT IS READ AS F OF G , WHERE F AND G ARE<BR>\n" );
document.write( "SYMBOLS FOR DIFFERENT FUNCTIONS.<BR>\n" );
document.write( "NOW WHAT IS A FUNCTION?IT IS SOME THING LIKE A<BR>\n" );
document.write( "RELATION-BUT A LITTLE<BR>\n" );
document.write( "MORE DEMANDING THAN THAT.LET US SEE.. SUPPOSE THE<BR>\n" );
document.write( "FUNCTION F OF MEANS<BR>\n" );
document.write( "FATHER OF....SAY JOHN IS FATHER OF EMMA..THEN F OF E<BR>\n" );
document.write( "MEANING F OF<BR>\n" );
document.write( "EMMA OR FATHER OF EMMA IN FULL....IS A FUNCTION<BR>\n" );
document.write( "BECAUSE BESIDES BEING<BR>\n" );
document.write( "A RELATION IT GIVES US A UNIQUE ANSWER. NAMELY JOHN<BR>\n" );
document.write( "AND JOHN ONLY<BR>\n" );
document.write( "...BUT JOHN'S DAUGHTER IS EMMA IS A RELATION ,AND NOT<BR>\n" );
document.write( "A FUNCTION<BR>\n" );
document.write( "BECAUSE THE ANSWER IS NOT UNIQUE...THERE MAY BE<BR>\n" );
document.write( "ANOTHER TANYA DAUGHTER<BR>\n" );
document.write( "OF JOHN...SO WE MAY GET MORE THAN ONE ANSWER.THEN IT<BR>\n" );
document.write( "IS A RELATION BUT<BR>\n" );
document.write( "NOT FUNCTION.GOT IT.WE GENERALLY USE SYMBOLS,F,G<BR>\n" );
document.write( "ETC..TO DENOTE<BR>\n" );
document.write( "FUNCTIONS.IN THE SAME PROBLEM IF WE HAVE TO DEAL WITH<BR>\n" );
document.write( "MORE THAN 1<BR>\n" );
document.write( "FUNCTION AS IS IN THIS PROBLEM,WE USE F & G TO DENOTE<BR>\n" );
document.write( "2 DIFFERENT<BR>\n" );
document.write( "FUNCTIONS.F MAY BE FATHER OF AND G MAY BE MOTHER OF<BR>\n" );
document.write( "...ETC...<BR>\n" );
document.write( "NEXT WHAT IS F OF G ..SAME MEANING ..IT MEANS FATHER<BR>\n" );
document.write( "OF MOTHER OF SOME<BR>\n" );
document.write( "BODY SPECIFIED IN THE PROBLEM SAY MARIE...SO IT MEANS<BR>\n" );
document.write( "FATHER OF MOTHER<BR>\n" );
document.write( "OF MARIE.THAT IS ALL TO IT.<BR>\n" );
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document.write( "SO IF WE WRITE THE GIVEN EQN.AS <BR>\n" );
document.write( "Y^2=X^2-1<BR>\n" );
document.write( "Y=SQRT(X^2-1)=+ OR - SQRT(X^2-1)<BR>\n" );
document.write( "THEN WE END UP WITH 2 VALUES OF Y FOR ONE VALUE OF X .SO THE ANSWER IS NOT UNIQUE AND IT WILL NOT BE A FUNCTION.<BR>\n" );
document.write( "WE CAN MAKE IT A FUNCTION BY DEFINING IT AS <BR>\n" );
document.write( "Y=|SQRT(X^2-1)| </SPAN>\n" );
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