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KCET2012MathematicsInverse Trigonometric Functions

2 ⁻¹ x= ⁻¹ (2 x 1-x² ) is valid for all values of x satisfying

Options

  1. A-1 x 1
  2. B0 x 1
  3. C1 2 x 1
  4. D0 x 1 2

Correct answer

C. 1 2 x 1

Step-by-step solution

Put ⁻¹ x=y , so that x= y Then, 0 y and |x| 1 and the RHS of given equation becomes ⁻¹(2 y y)= ⁻¹( 2 y)=2 y Since, ⁻¹ (2 x 1-x² ) lies between - 2 and 2 2 y lies between - 2 and 2 . i.e., y lies between - 4 and 4 . - 4 y 4 On combining Eqs. (i) and (ii), we get array r 0 y 4 1 y 1 2 1 2 x 1 x [ 1 2 , 1 ] array

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