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this question is from arihant amit M agarwal continuity and differentiability

this question is from arihant amit M agarwal continuity and differentiability
 
 

Question Image
Grade:12

1 Answers

yog
19 Points
3 years ago
f(x+y) + f(x-y) = 2f(x)f(y)
now put y=0
we get
f(x) + f(x) = 2kf(x) 
f(x)(k-1)=0 
either k=1 or f(x)=0.
if k=0 then f(x)=0 i.e niether odd nor even 
now put x=0
we get f(y) + f(-y) = 2kf(y)
put k=1 ( for any other value of k, f is 0)
 f(y) + f(-y) = 2f(y),  f(-y)= -f(y) thus for k=1 f is odd 

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