The value of ⁻¹(1) + ⁻¹ ( 1 2 ) + ⁻¹ ( 1 2 ) ⁻¹( 3 ) - ⁻¹(-2) is equal to

Step-by-step solution

The given expression is ⁻¹(1) + ⁻¹ ( 1 2 ) + ⁻¹ ( 1 2 ) ⁻¹( 3 ) - ⁻¹(-2) Evaluating the terms in the numerator: ⁻¹(1) = 4 Using the identity ⁻¹(x) + ⁻¹(x) = 2 , we have ⁻¹ ( 1 2 ) + ⁻¹ ( 1 2 ) = 2 Numerator = 4 + 2 = 3 4 Evaluating the terms in the denominator: ⁻¹( 3 ) = 3 ⁻¹(-2) = - ⁻¹(2) = - 3 = 2 3 Denominator = 3 - 2 3 = - 3 Substituting these values back into the expression: 3 4 - 3 = 3 4 (- 3 ) = - 9 4 Answer: -9 4