Let f: R R and g: R R be functions satisfying f(x + y) = f(x)...

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Let f: R R and g: R R be functions satisfying f(x + y) = f(x) + f(y) + f(x)f(y) and f(x) = xg(x) for all x, y R. If lim g(x) = 1, then which of the following statements is/are TRUE? (A) fis differentiable at every x ER (B) If g(0) = 1, then g is differentiable at every x = R (C) The derivative f(1) is equal to 1 (D) The derivative f(0) is equal to 1 Let f: R R and g: R R be functions satisfying f(x + y) = f(x) + f(y) + f(x)f(y) and f(x) = xg(x) for all x, y R. If lim g(x) = 1, then which of the following statements is/are TRUE? (A) fis differentiable at every x ER (B) If g(0) = 1, then g is differentiable at every x = R (C) The derivative f(1) is equal to 1 (D) The derivative f(0) is equal to 1

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