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Let f(x2 + y) = (f(x)) 2 + f(y) for all x, y  R, then

(A) f(x) is odd

(B) f(x) is even  f(x) = 0  x  R

(C) f(x) is continuous at x = 0  it is continuous everywhere

(D) f(x) is differentiable at x = 0  f(x) = x f '(0),  x  R

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Correct option (A)(B)(C)(D)


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