Consider the following statements: 1. ⁻¹ x+ ⁻¹ ( 1 x )= 2. There exist x, y [-1,1] , where x y such that ⁻¹ x+ ⁻¹ y= 2 Which of the above statements is/are correct?

Step-by-step solution

Statement-1 aligned & ( ⁻¹ x+ ⁻¹ y= ⁻¹ x+y 1-x y ) & aligned ⁻¹ x+ ⁻¹ 1 x & = ⁻¹ x+ 1 x 1-x 1 x & = ⁻¹ x^2+1 0 & = ⁻¹ = ⁻¹ 2 aligned aligned ⁻¹ x+ ⁻¹ 1 x = 2 Statement (1) is wrong. Statement 2, ⁻¹ x+ ⁻¹ y= 2 (x, y) (-1,1) Only when x=y Here x y . Statement (2) is also wrong.