If X = ⁻¹ [2 (2 ⁻¹ 1 2 ) ] + ⁻¹ [ ( 7 6 ) ] and Y = ⁻¹ [ ( 11 6 ) ] + ⁻¹ [ ( 4 3 ) ] then the value of 2X - Y is:

Step-by-step solution

Evaluating the first expression X : ⁻¹ ( 1 2 ) = 6 ⁻¹ [2 (2 ( 6 ) ) ] = ⁻¹ [2 ( 3 ) ] = ⁻¹ (2 ( 1 2 ) ) = ⁻¹(1) = 4 For the second term of X , the principal value branch of ⁻¹ is [0, ] : ⁻¹ [ ( 7 6 ) ] = ⁻¹ [ (2 - 5 6 ) ] = ⁻¹ [ ( 5 6 ) ] = 5 6 Thus, X = 4 + 5 6 = 13 12 Evaluating the second expression Y : The principal value branch of ⁻¹ is [- 2 , 2 ] : ⁻¹ [ ( 11 6 ) ] = ⁻¹ [ (2 - 6 ) ] = ⁻¹ [- ( 6 ) ] = - 6 The principal value branch of ⁻¹ is (- 2 , 2 ) : ⁻¹ [ ( 4 3 ) ] = ⁻¹ [ ( + 3 ) ] = ⁻¹ [ ( 3 ) ] = 3 Thus, Y