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Q 1639645512.     Let `f:(0,1)\rightarrow \mathbb{R}` be defined by` f(x)=\frac{b-x}{1-bx}`, where b is a constant such that `0 < b < 1.`

JEE 2011 ADVANCED Paper - 2

(This question may have multiple correct answers)

A `f` is not invertible on `(0,1)`
B `f\ne f^{-1}` on `(0,1) and f'(b)= - \frac{1}{f'(0)}`
C `f=f^{-1}` on `(0,1) and f'(b)= \frac{1}{f'(0)}`
D `f^{-1}` is differentiable on `(0,1)`
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