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If g(x) is continuous function in `[0, oo)` satisfying `g(1) = 1. If int_(0)^(x) 2x . g^(2)(t)dt = (int_(0)^(x) 2g(x - t)dt)^(2)`, find g(x).

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`[0, oo)`
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ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Questions Asked In Previous 13 Years Exam)
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