If the domain of \( f(x)=\frac{1}{\pi} \cos ^{-1}\left[\log _{3}\left(\frac{x^{2}}{3}\right)\rig...

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If the domain of \( f(x)=\frac{1}{\pi} \cos ^{-1}\left[\log _{3}\left(\frac{x^{2}}{3}\right)\right] \) where, \( x0 \) is \( [a, b] \) and the range of \( f(x) \) is \( [c, d] \), then:
(a) \( a, b \) are the roots of the equation \( x^{4}-3 x^{3}-x+3=0 \)
(b) \( a, b \) are the roots of the equation \( x^{4}-x^{3}+x^{2}-2 x+1=0 \)
(c) \( a^{3}+d^{3}=1 \)
(d) \( a^{2}+b^{2}+c^{2}+d^{2}=11 \)
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