If 0 ⁻¹ x and - 2 ⁻¹ x 2 , then at x= 1 5 the value of (2 ⁻¹ x+ ⁻¹ x ) is

Step-by-step solution

Given (2 ⁻¹ x + ⁻¹ x) at x = 1 5 , observe that 2 ⁻¹ x + ⁻¹ x = ⁻¹ x + ( ⁻¹ x + ⁻¹ x) = ⁻¹ x + 2 since ⁻¹ x + ⁻¹ x = 2 for x [-1, 1] . Thus, the expression simplifies to ( ⁻¹ x + 2 ) = - ( ⁻¹ x) using the identity ( + 2 ) = - . Since ( ⁻¹ x) = 1 - x^2 for x [-1, 1] , the expression becomes - 1 - x^2 . Substituting x = 1 5 yields - 1 - ( 1 5 )^2 = - 1 - 1 25 = - 24 25 . The value is - 24 25 , corresponding to option A.