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The domain of the function [JEE Main-2021 (August)] \( f(x)=\sin ^{-1}\left(\frac{3 x^{2}+x-1}{(x-1)^{2}}\right)+\cos ^{-1}\left(\frac{x-1}{x+1}\right) \) is :
\( \mathrm{P} \)
IV
(a) \( \left[0, \frac{1}{4}\right] \)
(b) \( [-2,0] \cup\left[\frac{1}{4}, \frac{1}{2}\right] \)
(c) \( \left[\frac{1}{4}, \frac{1}{2}\right] \cup\{0\} \)
(d) \( \left[0, \frac{1}{2}\right] \)
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