23na re ans key is wrng , see f(x) = cosx satisfies the functional relation , wich is even
F(X+Y) + F(X-Y)=2F(X)F(Y),X,Y ≡R AND F(0)=K??
THEN WHICH IS TRUE??
A)F IS EVEN IF K=1
B)F IS ODD IF K=0
C)F IS ALWAYS ODD
D)NONE OF THESE
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4 Answers
23put x = 0 ,
then f(y)+f(-y) = 2f(y)k
for k = 1 ,f is even
for k = 0 , f is odd , provided f is not 0 through out the domain.
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