Question 64635: Explain why an even function f does not have an inverse f-1 (f exponeant -1)
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Explain why an even function f does not have an inverse f-1 (f exponeant -1)
F(X) IS EVEN FUNCTION IF
F(X)=F(-X)
LET US DO AN EXAMPLE
SAY Y=F(X)=X^2=F(-X)=(-X)^2=X^2...IS AN EVEN FUNCTION
IF WE TRY TO FIND THE INVERSE
Y=X^2
X=SQRT(Y)
HENCE F INVERSE (X) IS SQRT(X)
SQRT(X) IS NOT A FUNCTION AS IT LEADS TO MULTIPLE IMAGES
SQRT(4)=+2....OR......-2.
HENCE ONLY IF WE DEFINE IT AS |SQRT(X)|,IT CAN BE CALLED A FUNCTION.OTHERWISE IT IS A RELATION , BUT NOT A FUNCTION.
THAT IS,IN GENERAL SINCE F(X) AND F(X) CORRESPOND TO SAME VALUE OF Y,THE INVERSE WILL NOT BE A FUNCTION,BUT A RELATION AS IT LEADS TO NOT UNIQUE BUT MULTIPLE IMAGES.
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