Let \( f(x)=\cos ^{-1}\left(2 x^{2}-1\right) \) then : (a) \( f(x) ...

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Let \( f(x)=\cos ^{-1}\left(2 x^{2}-1\right) \) then :
(a) \( f(x) \) is continuous in \( [-1,1] \)
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(b) \( f(x) \) is derivable in \( (-1,1) \)
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(c) range of \( f(x) \) is \( (0, \pi) \)
(d) derivative of \( f(x) \) w.r.t. \( \sin ^{-1} x \) at \( x=\frac{1}{2} \) is 2
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