\( f(x)=\sqrt{x-1}+\sqrt{2-x} \) and \( g(x)=x^{2}+1 x+c \) are two given functions such that \(...

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\( f(x)=\sqrt{x-1}+\sqrt{2-x} \) and \( g(x)=x^{2}+1 x+c \) are two given functions such that \( f(x) \) and \( g(x) \) ali,in their maximum and minimum values respectively for same value of \( x \), then
(a) \( f(x)_{\max } \) at \( x=\frac{1}{2} \)
(b) \( f(x)_{\max } \) at \( x=\frac{3}{2} \)
(c) \( b=3 \)
(d) \( b=-3 \)
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