If ⁻¹ x= ,(0 < x < 1) and ⁻¹ (2 x 1-x² )+ ⁻¹ ( 1 2 x²-1 )= 2 3 , then ⁻¹(2 x)=

Step-by-step solution

Given that, ⁻¹ x= ,(0 < x < 1)...(i) x= Thus, ⁻¹ (2 x 1-x² )+ ⁻¹ ( 1 2 x²-1 )= 2 3 aligned ⁻¹ (2 .1- ² ) . &+ ⁻¹ ( 1 2 ² -1 )= 2 3 aligned aligned & ⁻¹( 2 )+ ⁻¹( 2 )= 2 3 & 2 +2 = 2 3 = 6 aligned Now, x= 6 = 3 2 2 x= 3 Therefore, ⁻¹(2 x)= ⁻¹ 3 = 3