Determine whether Even or Odd: f(x+y) + f(x-y) = 2f(x).f(y); where f(0) is not zero and x, y belongs to set of real numbers.

Question
Determine whether Even or Odd:
f(x+y) + f(x-y) = 2f(x).f(y); where f(0) is not zero and x, y belongs to set of real numbers.

Answer
f(x+y) + f(x-y) = 2*f(x)*f(y) .............. (1)

First let us put x=y=0 in equation (1).
This gives us :
2 * f(0) = 2*f(0)*f(0) , So ,
f(0)=1 (as it is given f(0) not equal to 0)

Now, let us put x = 0 in equation (1)
This gives us :
f(y) + f(-y) = 2*f(y)*f(0)
f(y) + f(-y) = 2*f(y)
f(-y) = f(y)

Hence, the function is Even.