Verified answer

5f(x) = 3f(1/x) + 1/√x  (x> 0)

подставим вместо х значение 1/x

5f(1/x) = 3f(x) + 1/√(1/x) |*3

3f(1/x) = 5f(x) - 1/√x  |*5

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15f(1/x) = 9f(x) + 3√x

15f(1/x) = 25f(x) - 5/√x

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25f(x) - 9f(x) - 5/√x - 3√x = 0

16f(x) = 5/√x + 3√x

f(x) = (5/√x + 3√x)/16