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Question

Suppose f and g are differentiable functions on (0,) such that f'(x)=g(x)x and g'(x)=f(x)x, for all x>0. Further, f(1)=3 and g(1)=1.

If f(x)+g(x)=Axk, for all x>0 and some constant A, then the value of k equals

A
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B
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C
1
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D
2
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