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Functions question

2011 · Shift 2 · Q37
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Functions question

2011 · Shift 2 · Q37

JEE AdvancedMathematicsFunctionsMultiple correct+4 / −1
Let f:(0,1)→Rf:(0,1) \to Rf:(0,1)→R be defined by f(x)=b−x1−bxf(x) = {{b - x} \over {1 - bx}}f(x)=1−bxb−x​, where b is a constant such that 0<b<10 \lt b \lt 10<b<1. Then
  1. A
    f is not invertible on (0, 1).
  2. B
    f eee f −-− 1 on (0, 1) and f′(b)=1f′(0)f'(b) = {1 \over {f'(0)}}f′(b)=f′(0)1​.
  3. C
    f = f −-− 1 on (0, 1) and f′(b)=1f′(0)f'(b) = {1 \over {f'(0)}}f′(b)=f′(0)1​.
  4. D
    f −-− 1 is differentiable on (0, 1).
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