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Question 65964: I could really use some help with this one:
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:
a. f(x) = 2 if x>1
f(x) = -1 otherwise
b. f(x) = 5 if x>0
f(x) = -5 if x<0
f(x) = 5 or -5 if x = 0
c. f(x) = 10/x
Thank you.
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! I could really use some help with this one:
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:
a. f(x) = 2 if x>1
f(x) = -1 otherwise
b. f(x) = 5 if x>0
f(x) = -5 if x<0
f(x) = 5 or -5 if x = 0
c. f(x) = 10/x
Thank you.
IF YOU LIKE TO KNOW ABOUT FUNCTION VS RELATION READ THE FOLLOWING.ANSWER TO YOUR QUESTIONS FOLLOW.
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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.
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a. f(x) = 2 if x>1
f(x) = -1 otherwise
TEST IS TO FIND FOR A PARTICULAR VALUE OF X THERE ARE 2 VALUES
OF F(X) OR Y IN SHORT.THAT IS FOR ANY X=A SAY THERE SHOULD CORRESPOND
ONE AND ONLY ONE VALUE OF Y SAY B.IF Y1 AND Y2 ARE DISTINCT THEN BOTH
SHOULD NOT BE DERIVED FROM SAME VALUE OF X.IN OTHER WORDS Y1 SHOULD
EQUAL Y2 IF THEY BOTH CORRESPOND TO SAME VALUE OF X.
HERE THE TEST IS SATISFIED. HENCE F(X) IS A FUNCTION.
IMPORTANT....NOTE THAT X1,X2,X3..ETC....MAY HAVE SAME VALUE OF Y SAY B.
IT DOES NOT MATTER.BUT SAME VALUE OF X SAY A SHOULD NOT LEAD TO
Y1,Y2,ETC.THEN ....Y1 SHOULD EQUAL Y2..ETC.
b. f(x) = 5 if x>0
f(x) = -5 if x<0
f(x) = 5 or -5 if x = 0
SAME TEST ..IT IS NOT A FUNCTION.SINCE,HERE WE ARE GIVEN THAT
F(X)=5 OR -5
AT X=0..THAT IS SAME VALUE OF X CORRESPONDS TO Y1 & Y2.
c. f(x) = 10/x
SAME TEST IT IS A FUNCTION.HOWEVER IT IS NOT DEFINED AT X=0.SO WE SAY
THE DOMAIN EXCLUDES X=0..FOR ANY OTHER REAL VALUE OF X IT IS A FUNCTION.
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