Question 38632
PLEASE FIND BELOW EXPLANATION ON FUNCTION,RELATION AND FUNCTION OF A FUNCTION..FROM GENERAL ENGLISH AND MATHHEMATICALLY SPEAKING.
NOW COMING TO F O G IN ENGLISH.LET ME TRY..
FISTLY IT IS READ AS F OF G , WHERE F AND G ARE SYMBOLS FOR DIFFERENT FUNCTIONS.
NOW WHAT IS A FUNCTION?IT IS SOME THING LIKE A RELATION-BUT A LITTLE
MORE DEMANDING THAN THAT.LET US SEE.. SUPPOSE THE FUNCTION F OF MEANS
FATHER OF....SAY  JOHN IS FATHER OF EMMA..THEN F OF E MEANING F OF
EMMA OR FATHER OF EMMA IN FULL....IS A FUNCTION BECAUSE BESIDES BEING
A RELATION IT GIVES US A UNIQUE ANSWER. NAMELY JOHN AND JOHN ONLY
...BUT JOHN'S DAUGHTER IS EMMA IS A RELATION ,AND  NOT A FUNCTION
BECAUSE THE ANSWER IS NOT UNIQUE...THERE MAY BE ANOTHER TANYA DAUGHTER
OF JOHN...SO WE MAY GET MORE THAN ONE ANSWER.THEN IT IS A RELATION BUT
NOT FUNCTION.GOT IT.WE GENERALLY USE SYMBOLS,F,G ETC..TO DENOTE
FUNCTIONS.IN THE SAME PROBLEM IF WE HAVE TO DEAL WITH MORE THAN 1
FUNCTION AS IS IN THIS PROBLEM,WE USE F & G TO DENOTE 2 DIFFERENT
FUNCTIONS.F MAY BE FATHER OF AND G MAY BE MOTHER OF ...ETC...
NEXT WHAT IS F OF G ..SAME MEANING ..IT MEANS FATHER OF MOTHER OF SOME
BODY SPECIFIED IN THE PROBLEM SAY MARIE...SO IT MEANS FATHER OF MOTHER
OF MARIE.THAT IS ALL TO IT.
LET US GET ON TO OUR PROBLEM NOW  AND GO STEP BY STEP.
F(X)=2X-3.....AND G(X)=-X+3.....HERE X IS CALLED INDEPENDENT VARIABLE
.IT CAN TAKE ANY VALUE (LEGALLY PERMITTED..WE SKIP THIS ASPECT FOR THE
PRESENT)..SUPPOSE X=1..THEN F(X) IS CALLED DEPENDENT VARIABLE SINCE
ITS VALUE DEPENDS ON VALUE OF X.IF X=1,THEN F(1)=2*1-3=2-3=-1...THAT
IS WE JUST PUT THAT VALUE OF X (1 AS WE TOOK )IN PLACE OF X WHEREVER
IT OCCURS IN THE FUNCTION..
SO F(1)=-1...SIMILARLY...F(0)=2*0-3=-3...ETC
SAME THING APPLIES TO G(X) OR F OF G OF X ..IN SEQUENCING THE ORDER OF
OPERATIONS ,FOR CONVENIENCE ,WE COME FROM INSIDE TO OUT SIDE..LIKE AS
WE DO IN ENGLISH EXAMPLE MENTIONED ABOVE...FATHER OF MOTHER OF
MARIE..WE FIRST FIND MOTHER OF MARIE AND THEN HER FATHER.SAME WAY TO
FIND
F OF G(2)..LET US FIND G(2) FIRST..G(X)=-X+3
G(2)=-2+3=1...HENCE NOW WE HAVE TO FIND
F(1)=2*1-3=-1
WELL THAT IS THE END OF IT.HOPE IT IS CLEAR.