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

A function f satisfies the condition `f(x)=f'(x)+f''(x)+f'''(x)+…,` where f(x) is a differentiable function indefinitely and dash denotes the order the derivative. If f(0) = 1, then f(x) is

`e^(x//2)`

`e^(x)`

`e^(2x)`

`e^(4x)`

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AI Generated Solution

To solve the problem, we start with the given condition for the function \( f(x) \): \[ f(x) = f'(x) + f''(x) + f'''(x) + \ldots \] ### Step 1: Set up the equation We can express this condition as: ...

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