it is siple and logical question.

Putting x = y = 0, we get
f(0) = f2(0) - f2(a) and since f(0) = 1, we get f(a) = 0
Putting x = 0, we get f(-y) = f(y) i.e. f is an even function
interchanging x and y, we get 
Since f is even f(x-y) = f(y-x), which gives us 
Now put x = a and we get 
Now in the original equation, put x = a and y = -a to get f(2a) = -1
means 
Now put y = x-a and you get 
hence- 
good question.
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