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`        Let f:R-R be a function such that f (x+y)+f (x-y)=f (xy) for all x,y €R.Then f is:`
5 months ago

```							 Put y=0=> f(x)+f(x)=2f(x).f(0)=> f(0)=1Now put x=0 and y=x=> f(x)+f(-x)=2f(0)f(x)=> f(x)+f(-x)=2f(x)=> f(-x)=f(x)So, even function.
```
5 months ago
```							aruns ans is wrong.we are given that f(x+y) + f(x – y)= f(xy).... (1)put y=0then f(x)+f(x)= f(0)or f(x)= f(0)/2= C (a constant)so from (1),C+C=Cor C=0so that f(x)= 0 is the only possibility.
```
5 months ago
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