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Let f:(0,1) R be defined by f(x)= b-x 1-b x , where b is a constant such that 0 < b < 1 . Then,

Options

  1. Af if not invertible on (0,1)
  2. Bf f⁻¹ on (0,1) and f^ (b)= 1 f^ (0)
  3. Cf=f⁻¹ on (0,1) and f^ (b)= 1 f^ (0)
  4. Df⁻¹ is differentiable on (0,1)

Correct answer

A. f if not invertible on (0,1)

Step-by-step solution

Here, f(x)= b-x 1-b x where, 0 0 and b-y 1-b y 1 b (b-1)(y+1) 1-b y < -1 < y < 1 b gathered From Eqs. (i) and (ii), we get y (-1, 1 b ) Codomain Thus, f(x) is not invertible.

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