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f is a real valued function and not identically zero satisfying f(x+y)+f(x-y) = 2f(x)f(y) for all x,y belonging to R then it is what type of function even or odd ? How? f is a real valued function and not identically zero satisfying f(x+y)+f(x-y) = 2f(x)f(y) for all x,y belonging to R then it is what type of function even or odd ? How?
as we know for even functionf(x)=f(-x) and for odd function f(x)=-f(-x)ifPut 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.
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