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this question is from arihant amit M agarwal continuity and differentiability

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3 years ago

```							f(x+y) + f(x-y) = 2f(x)f(y)now put y=0we getf(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=0we 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
```
3 years ago
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