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Black Book Advanced Problems in MathematicsMathematicsContinuity and Differentiability

Suppose a function f(x) satisfies the following conditions f(x+y) = f(x) + f(y) 1 + f(x) f(y) , x, y R and f'(0) = 1 Also -1 < f(x) < 1 , x R f(x) increases in the complete interval :

Options

  1. A(- , -1) (-1, 0) (0, 1) (1, )
  2. B(- , )
  3. C(- , -1) (-1, 0)
  4. D(0, 1) (1, )

Correct answer

B. (- , )

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