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You can put this solution on YOUR website!
I could really use some help with this one:
\n" ); document.write( "Which of the following are functions? Explain your reasoning for a, b, and c. Keep the definition of a function strongly in mind as you so this problem. Think about whether the relationship between f(x) and x is consistent with being a function or not and explain your reasoning:
\n" ); document.write( "a. f(x) = 2 if x>1
\n" ); document.write( "f(x) = -1 otherwise
\n" ); document.write( "b. f(x) = 5 if x>0
\n" ); document.write( "f(x) = -5 if x<0
\n" ); document.write( "f(x) = 5 or -5 if x = 0
\n" ); document.write( "c. f(x) = 10/x
\n" ); document.write( "Thank you.
\n" ); document.write( "IF YOU LIKE TO KNOW ABOUT FUNCTION VS RELATION READ THE FOLLOWING.ANSWER TO YOUR QUESTIONS FOLLOW.
\n" ); document.write( "--------------------------------------------------------------------------------
\n" ); document.write( "PLEASE FIND BELOW EXPLANATION ON FUNCTION,RELATION AND
\n" ); document.write( "FUNCTION OF A FUNCTION..FROM GENERAL ENGLISH AND
\n" ); document.write( "MATHHEMATICALLY SPEAKING.
\n" ); document.write( "NOW COMING TO F O G IN ENGLISH.LET ME TRY..
\n" ); document.write( "FISTLY IT IS READ AS F OF G , WHERE F AND G ARE
\n" ); document.write( "SYMBOLS FOR DIFFERENT FUNCTIONS.
\n" ); document.write( "NOW WHAT IS A FUNCTION?IT IS SOME THING LIKE A
\n" ); document.write( "RELATION-BUT A LITTLE
\n" ); document.write( "MORE DEMANDING THAN THAT.LET US SEE.. SUPPOSE THE
\n" ); document.write( "FUNCTION F OF MEANS
\n" ); document.write( "FATHER OF....SAY JOHN IS FATHER OF EMMA..THEN F OF E
\n" ); document.write( "MEANING F OF
\n" ); document.write( "EMMA OR FATHER OF EMMA IN FULL....IS A FUNCTION
\n" ); document.write( "BECAUSE BESIDES BEING
\n" ); document.write( "A RELATION IT GIVES US A UNIQUE ANSWER. NAMELY JOHN
\n" ); document.write( "AND JOHN ONLY
\n" ); document.write( "...BUT JOHN'S DAUGHTER IS EMMA IS A RELATION ,AND NOT
\n" ); document.write( "A FUNCTION
\n" ); document.write( "BECAUSE THE ANSWER IS NOT UNIQUE...THERE MAY BE
\n" ); document.write( "ANOTHER TANYA DAUGHTER
\n" ); document.write( "OF JOHN...SO WE MAY GET MORE THAN ONE ANSWER.THEN IT
\n" ); document.write( "IS A RELATION BUT
\n" ); document.write( "NOT FUNCTION.GOT IT.WE GENERALLY USE SYMBOLS,F,G
\n" ); document.write( "ETC..TO DENOTE
\n" ); document.write( "FUNCTIONS.IN THE SAME PROBLEM IF WE HAVE TO DEAL WITH
\n" ); document.write( "MORE THAN 1
\n" ); document.write( "FUNCTION AS IS IN THIS PROBLEM,WE USE F & G TO DENOTE
\n" ); document.write( "2 DIFFERENT
\n" ); document.write( "FUNCTIONS.F MAY BE FATHER OF AND G MAY BE MOTHER OF
\n" ); document.write( "...ETC...
\n" ); document.write( "NEXT WHAT IS F OF G ..SAME MEANING ..IT MEANS FATHER
\n" ); document.write( "OF MOTHER OF SOME
\n" ); document.write( "BODY SPECIFIED IN THE PROBLEM SAY MARIE...SO IT MEANS
\n" ); document.write( "FATHER OF MOTHER
\n" ); document.write( "OF MARIE.THAT IS ALL TO IT.
\n" ); document.write( "LET US GET ON TO OUR PROBLEM NOW AND GO STEP BY STEP.
\n" ); document.write( "F(X)=2X-3.....AND G(X)=-X+3.....HERE X IS CALLED
\n" ); document.write( "INDEPENDENT VARIABLE
\n" ); document.write( ".IT CAN TAKE ANY VALUE (LEGALLY PERMITTED..WE SKIP
\n" ); document.write( "THIS ASPECT FOR THE
\n" ); document.write( "PRESENT)..SUPPOSE X=1..THEN F(X) IS CALLED DEPENDENT
\n" ); document.write( "VARIABLE SINCE
\n" ); document.write( "ITS VALUE DEPENDS ON VALUE OF X.IF X=1,THEN
\n" ); document.write( "F(1)=2*1-3=2-3=-1...THAT
\n" ); document.write( "IS WE JUST PUT THAT VALUE OF X (1 AS WE TOOK )IN PLACE
\n" ); document.write( "OF X WHEREVER
\n" ); document.write( "IT OCCURS IN THE FUNCTION..
\n" ); document.write( "SO F(1)=-1...SIMILARLY...F(0)=2*0-3=-3...ETC
\n" ); document.write( "SAME THING APPLIES TO G(X) OR F OF G OF X ..IN
\n" ); document.write( "SEQUENCING THE ORDER OF
\n" ); document.write( "OPERATIONS ,FOR CONVENIENCE ,WE COME FROM INSIDE TO
\n" ); document.write( "OUT SIDE..LIKE AS
\n" ); document.write( "WE DO IN ENGLISH EXAMPLE MENTIONED ABOVE...FATHER OF
\n" ); document.write( "MOTHER OF
\n" ); document.write( "MARIE..WE FIRST FIND MOTHER OF MARIE AND THEN HER
\n" ); document.write( "FATHER.SAME WAY TO
\n" ); document.write( "FIND
\n" ); document.write( "F OF G(2)..LET US FIND G(2) FIRST..G(X)=-X+3
\n" ); document.write( "G(2)=-2+3=1...HENCE NOW WE HAVE TO FIND
\n" ); document.write( "F(1)=2*1-3=-1
\n" ); document.write( "WELL THAT IS THE END OF IT.HOPE IT IS CLEAR.
\n" ); document.write( "--------------------------------------------------------------------------------
\n" ); document.write( "a. f(x) = 2 if x>1
\n" ); document.write( "f(x) = -1 otherwise
\n" ); document.write( "TEST IS TO FIND FOR A PARTICULAR VALUE OF X THERE ARE 2 VALUES
\n" ); document.write( "OF F(X) OR Y IN SHORT.THAT IS FOR ANY X=A SAY THERE SHOULD CORRESPOND
\n" ); document.write( "ONE AND ONLY ONE VALUE OF Y SAY B.IF Y1 AND Y2 ARE DISTINCT THEN BOTH
\n" ); document.write( "SHOULD NOT BE DERIVED FROM SAME VALUE OF X.IN OTHER WORDS Y1 SHOULD
\n" ); document.write( "EQUAL Y2 IF THEY BOTH CORRESPOND TO SAME VALUE OF X.
\n" ); document.write( "HERE THE TEST IS SATISFIED. HENCE F(X) IS A FUNCTION.
\n" ); document.write( "IMPORTANT....NOTE THAT X1,X2,X3..ETC....MAY HAVE SAME VALUE OF Y SAY B.
\n" ); document.write( "IT DOES NOT MATTER.BUT SAME VALUE OF X SAY A SHOULD NOT LEAD TO
\n" ); document.write( "Y1,Y2,ETC.THEN ....Y1 SHOULD EQUAL Y2..ETC.
\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( "b. f(x) = 5 if x>0
\n" ); document.write( "f(x) = -5 if x<0
\n" ); document.write( "f(x) = 5 or -5 if x = 0
\n" ); document.write( "SAME TEST ..IT IS NOT A FUNCTION.SINCE,HERE WE ARE GIVEN THAT
\n" ); document.write( " F(X)=5 OR -5
\n" ); document.write( "AT X=0..THAT IS SAME VALUE OF X CORRESPONDS TO Y1 & Y2.
\n" ); document.write( "c. f(x) = 10/x
\n" ); document.write( "SAME TEST IT IS A FUNCTION.HOWEVER IT IS NOT DEFINED AT X=0.SO WE SAY
\n" ); document.write( "THE DOMAIN EXCLUDES X=0..FOR ANY OTHER REAL VALUE OF X IT IS A FUNCTION. \n" ); document.write( "