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The correct answer is **III. (c) f(x) is a periodic function**.

The Fourier series of a function is only possible if the function is periodic.

Fourier series of f(x) in (0, 2π) is possible only when (a) f(x) is an even function, (b) f(x) is an odd function, (c) f(x) is a periodic function, (d) All of these.

Explore the conditions for the existence of a Fourier series, which is only possible when the function is periodic. Learn more about the mathematical concepts of Fourier Series and periodicity in this detailed explanation.

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