document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=84464>Question 84464</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I do not fully understand what domain is and I am having trouble with the following problem:\r<BR>\n" );
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document.write( "y= square root of(9-x^2) + square root of(1-x^2)\r<BR>\n" );
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document.write( "The answer on my key is domain=[1,3] but I do not understand why. Can you please explain? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #60832 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=60832\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I do not fully understand what domain is and I am having trouble with the following problem:<BR>\n" );
document.write( "y= square root of(9-x^2) + square root of(1-x^2)<BR>\n" );
document.write( "The answer on my key is domain=[1,3] but I do not understand why. Can you please explain?<BR>\n" );
document.write( "HERE X IS CALLED INDEPENDENT VARIABLE AND Y DEPENDENT VARIABLE.<BR>\n" );
document.write( "OUR UNIVERSE IS REAL NUMBERS FOR THIS PURPOSE.<BR>\n" );
document.write( "NOW , THIS DOES NOT MEAN THAT X CAN TAKE ANY VALUE IN REAL NUMBERS.<BR>\n" );
document.write( "IT CAN TAKE ONLY SUCH VALUES WHICH MAKE THE GIVEN FUNCTION F(X) OR Y IN SHORT MEANINGFUL.THAT IS A MATHEMATICALLY ALLOWED OPERATION.<BR>\n" );
document.write( "CERTAIN OPERATIONS LIKE DIVISION BY ZERO , SQUARE ROOT OF A NEGATIVE NUMBER,LOG OF ZERO OR NEGATIVE NUMBER ARE NOT DEFINED.EITHER THEY ARE CALLED INFINITY(PLUS OR MINUS)OR IMAGINARY.<BR>\n" );
document.write( "SO WE SAY X CAN NOT TAKE SUCH VALUES WHICH REQUIRES US TO PERFORM SUCH OPERATIONS.  <BR>\n" );
document.write( "X CAN TAKE VALUES OF ALL OTHER REAL NUMBERS.THE SET OF THESE REAL NUMBERS IS CALLED DOMAIN OF THE FUNCTION.<BR>\n" );
document.write( "IF YOU HAVE <BR>\n" );
document.write( "Y=1/(X-3)...DOMAIN IS ALL REAL VALUES EXCEPT 3 AS IT WILL LEAD TO DIVISION BY ZERO .<BR>\n" );
document.write( "IN YOUR EXAMPLE THE FIRST TERM BECOMES MEANING LESS IF<BR>\n" );
document.write( "9-X^2<0.HENCE<BR>\n" );
document.write( "9-X^2>=0<BR>\n" );
document.write( "9>=X^2<BR>\n" );
document.write( "X^2<=9<BR>\n" );
document.write( "|X|<=3......THAT IS X SHOULD BE BETWEEN -3 AND +3<BR>\n" );
document.write( "WE SHOW IT AS X = [-3,3]......[..]..BRACKETS INDICATE X CAN EQUAL THE BORDER VALUES <BR>\n" );
document.write( "THAT IS X=3 AND X=-3 ARE ALLOWED.<BR>\n" );
document.write( "NOW THERE IS A SECOND TERM.SQRT.(1-X^2)<BR>\n" );
document.write( "SIMILAR ARGUMENT LEADS US TO CONCLUDE X = [-1,1]<BR>\n" );
document.write( "THE COMBINATION OF THE I AND II CONDITIONS MAKE US TO CONCLUDE THAT X = [-1,1]<BR>\n" );
document.write( "YOUR ANSWER IS [1,3]WHICH IS NOT CORRECT.<BR>\n" );
document.write( "ON THE OTHER HAND,IF SECOND TERM IS SQ.RT(X^2-1)....THEN |X| >=|<BR>\n" );
document.write( "X<=-1......OR............X>=1...COMBINING THIS WITH I CONDITION , WE GET <BR>\n" );
document.write( "X=[1,3] AND [-3,-1] </SPAN>\n" );
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