|
Question 39601: Please explain to me how this equation can be a function
x^2=1+y^2
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Please explain to me how this equation can be a function
x^2=1+y^2
-------------------------------------------------------------------------------
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.
------------------------------------------------------------------------------
SO IF WE WRITE THE GIVEN EQN.AS
Y^2=X^2-1
Y=SQRT(X^2-1)=+ OR - SQRT(X^2-1)
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.
WE CAN MAKE IT A FUNCTION BY DEFINING IT AS
Y=|SQRT(X^2-1)|
|
|
|
| |
