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AP EAMCET202123 Aug 2021Morning ShiftMathematicsFunctionsActual

For what values of x , the following identity is valid and holds? tan h ⁻¹(x)= 1 2 _e ( 1+x 1-x ) .

Options

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

Correct answer

D. (-1,1)

Step-by-step solution

⁻¹ x- 1 2 _e ( 1+x 1-x ) When x=1 identity does not hold as _e ( 2 0 ) will form. At x=-1 also identity does not hold as _e ( 0 -2 ) will form and _e 0 does not exist. When x 1 , then 1+x 1-x becomes negative, then identity fails to exist. Identity valid only for x (-1,1) .

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