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

A

f is not invertible on (0, 1)

B

$$f \neq f^{-1}$$ 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)