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KCET2025MathematicsInverse Trigonometric Functions

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

Options

  1. A0 x 1 2
  2. B-1 x 1
  3. C0 x 1
  4. D1 2 x 1

Correct answer

D. 1 2 x 1

Step-by-step solution

aligned & 2 ⁻¹ x= ⁻¹ (2 x 1-x^2 ) & x= = ⁻¹ x & ⁻¹(2 )= ⁻¹( 2 )=2 [0,2 ] & =2 ⁻¹ x when [0, / 4] & 2 ⁻¹ x when ⁻¹ x [0, / 4] aligned 2 ⁻¹ x when x [ 1 2 , 1 ]

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