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A function f satisfies the condition f(x...

A function `f` satisfies the condition `f(x)=f^(prime)(x)+f''(x)+f'''(x)....`, where `f(x)` is an indefinitely differentiable function and dash denotes the order of derivatives. If `f(0)=1` ,then `f(x)` is
(a)`e^(x/2)` (b) `e^x` (c) `e^(2x)` (d) `e^(4x)`

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