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Manipal MET2013MathematicsInverse Trigonometric Functions

The interval for which 2 ⁻¹ x+ ⁻¹ 2 x 1+x^2 is independent of x is

Options

  1. A|x| 1
  2. B|x| 1
  3. C|x|=1
  4. Dф

Correct answer

B. |x| 1

Step-by-step solution

We know that; if |x| 1 , then 2 ⁻¹ x= ⁻¹ ( 2 x 1+x^2 ) and if |x| 1 , then -2 ⁻¹ x= ⁻¹ ( 2 x 1+x^2 ) thus, if |x| 1 . aligned 2 ⁻¹ x+ ⁻¹ 2 x 1+x^2 =2 ⁻¹ x+ -2 ⁻¹ x= aligned which is independent of x .

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