A function \( f \) satisfy the condition, \( f(x)=f^{\prime}(x)+f^{\prime \prime}(x) \) \( +f^{\...

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A function \( f \) satisfy the condition, \( f(x)=f^{\prime}(x)+f^{\prime \prime}(x) \) \( +f^{\prime \prime \prime}(x)+\cdots \) where \( f(x) \) is a differentiable function indefinitely and dash denotes the order of derivative. If \( f(0)=1 \), then \( f(x) \) is
(A) \( e^{x / 2} \)
(B) \( e^{x} \)
(C) \( e^{2 x} \)
(D) \( e^{4 x} \)
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