Even-Odd functions

Determine whether the following function is even or odd

f(x+y)+f(x-y)=2f(x)f(y).

f(0)â‰ 0.x,y are reals.

2 Answers

put y=x , f(2x) + f(0) = 2f(x)²

now put y=-x , f(0) + f(2x) = 2f(x)f(-x)

equate both sides , f(x) =0 or f(x) = f(-x)

both cases it's even.

Thank you very much for such a nice and compact solution.

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