Let \( g(x)=f(x)+f(1-x) \) and \( f^{\prime \prime}(x)0, \forall x \in(0,1) \). Then, \( g(x) \)...
Let \( g(x)=f(x)+f(1-x) \) and \( f^{\prime \prime}(x)0, \forall x \in(0,1) \). Then, \( g(x) \) is
(a) increasing on \( \left(0, \frac{1}{2}\right) \) and decreasing on \( \left(\frac{1}{2}, 1\right) \)
(b) increasing on \( \left(\frac{1}{2}, 1\right) \) and decreasing on \( \left(0, \frac{1}{2}\right) \)
(c) increasing on \( (0,1) \)
(d) decreasing on \( (0,1) \)
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