The function \( f(x)=2 \log (x-2)-x^{2}+4 x+1 \) increases on the interval (a) \( (1,2) \) (b) \...

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The function \( f(x)=2 \log (x-2)-x^{2}+4 x+1 \) increases on the interval
(a) \( (1,2) \)
(b) \( (2,3) \)
(c) \( (1,3) \)
(d) \( (2,4) \)
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