Let \( g(x)=a_{0}+a_{1} x+a_{2} x^{2}+a_{3} x^{3} \) and \( f(x)=\sqrt{g(x),} f(x) \) have its n...

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Let \( g(x)=a_{0}+a_{1} x+a_{2} x^{2}+a_{3} x^{3} \) and \( f(x)=\sqrt{g(x),} f(x) \) have its non-zero local minimum and maximum values at \( -3 \) and 3 , respectively. If \( a_{3} \in \) the domain of the function
\[
h(x)=\sin ^{-1}\left(\frac{1+x^{2}}{2 x}\right)
\]
The value of \( a_{0} \) is
(a) equal to 50
(b) greater than 54
(c) less than 54
(d) less than 50
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