SOLUTION: Decide whether each relation is a function. Explain. Y=x^4

Question 24271: Decide whether each relation is a function. Explain.
Y=x^4
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Y=X^4
LET US CONSIDER THIS IN OUR FIELD OF REAL NUMBERS.
TWO CONITIONS ARE TO BE SATISFIED FOR THIS RELATION TO BE AFUNCTION
1.FOR ALL X IN REAL NUMBERS ,THERE SHOULD BE A VALUE OF Y IN REAL NUMBERS.....THIS IS SATISFIED.
2.SAME VALUE OF X SHOULD NOT GIVE RAISE TO MORE THAN ONE VALUE OF Y ...THIS IS ALSO TRUE.
HENCE THIS IS A FUNCTION.
NOTE.....WE CAN HAVE SAME Y VALUE FOR MORE THAN ONE X VALUE AS IS THE CASE HERE.X=+1 GIVES Y=+1...AND X=-1 ALSO GIVES Y=+1..THIS IS OK.BUT THE OTHER WAY ROUND IS NOT ALLOWED FOR THE RELATION TO BE A FUNCTION.FOR EXAMPLE Y=SQRT.OF X IS NOT A FUNCTION SINCE X=+1 CAN GIVE RAISE TO 2 DIFFERENT VALUES OF Y NAMELY +1 AND -1.HENCE THIS IS NOT A FUNCTION.
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