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```
Ques1) Let f(x+y) + f(x-y) = 2 f(x) f(y), for all x,y belonging to R and f(0) = k ; then
(a) f is even if k=1
(b) f is odd if k=0
(c) f is always odd
(d) f is neither odd nor even for any value of k

```
10 years ago 147 Points
```							Dear Sanchit
f(x+y) + f(x-y) = 2 f(x) f(y), for all x,y belonging to R and f(0) = k
put x=0
f(y) + f(-y) = 2 f(0) f(y)
f(y) + f(-y) = 2 k f(y)
f(-y)=-(1-2k)f(y)
now for k=0
f(-y)=-f(y)
so f(y) is odd
and for k=1
f(-y)=f(y)
f(y) is even
so option a and b is correct

Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation.  All the best Sanchit Gupta.  Regards, Askiitians Experts Badiuddin
```
10 years ago
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