Let \( f:(0,1) \rightarrow R \) be defined by \( f(x)=\frac{b-x}{1-... VIDEO
Let \( f:(0,1) \rightarrow R \) be defined by \( f(x)=\frac{b-x}{1-b x} \), where \( b \) is a constant such that \( 0b1 \). Then
\( \mathrm{P} \)
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(A) \( f \) is not invertible on \( (0,1) \)
(B) \( f \neq f^{-1} \) on \( (0,1) \) and \( f^{\prime}(b)=\frac{1}{f^{\prime}(0)} \)
\( -(C) f=f^{-1} \) on \( (0,1) \) and \( f^{\prime}(b)=\frac{1}{f^{\prime}(0)} \)
(D) \( f^{-1} \) is differentiable on \( (0,1) \)
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