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The domain of the function \( f(x)=\sin ^{-1}\left(\frac{3 x^{2}+x-1}{(x-1)^{2}}\right)+\cos ^{-1}\left(\frac{x-1}{x+1}\…

Q1

The domain of the function \( f(x)=\sin ^{-1}\left(\frac{3 x^{2}+x-1}{(x-1)^{2}}\right)+\cos ^{-1}\left(\frac{x-1}{x+1}\right) \) is :

[JEE Main 2021, 31 Aug (Shift 2)]

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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