设lim_(x to 0) [1 + x + (f(x))/(x)]^(1)/(x) = e^3，则lim_(x to 0) [1 + (f(x))/(x)]^(1)/(x) = _____。

设 $ g(x) = \frac{f(x)}{x} $，则已知条件变为 \[ \lim_{x \to 0} \left[1 + x + g(x)\right]^{\frac{1}{x}} = e^3. \] 取对数得 \[ \lim_{x \to 0} \frac{1}{x} \ln \left[1 + x + g(x)\right] = 3. \] 由近似 $\ln(1+u) \approx u$（当 $u \to 0$），得 \[ \lim_{x \to 0} \frac{x + g(x)}{x} = 3 \implies \lim_{x \to 0} \left(1 + \frac{g(x)}{x}\right) = 3 \implies \lim_{x \to 0} \frac{g(x)}{x} = 2. \] 求目标极限 \[ \lim_{x \to 0} \left[1 + g(x)\right]^{\frac{1}{x}} = \lim_{x \to 0} e^{\frac{\ln(1+g(x))}{x}}. \] 由 $\ln(1+g(x)) \approx g(x)$（当 $g(x) \to 0$），得 \[ \lim_{x \to 0} \frac{\ln(1+g(x))}{x} = \lim_{x \to 0} \frac{g(x)}{x} = 2. \] 因此，目标极限为 $e^2$。 答案：$\boxed{e^2}$