⁻¹(x-1)+ ⁻¹(x-3)+ ⁻¹ ( x 2-x^2 )= ⁻¹ k+ , then the value of ' k ' is

Step-by-step solution

The domain of ⁻¹(x-1) is -1 x-1 1 , which implies 0 x 2 . The domain of ⁻¹(x-3) is -1 x-3 1 , which implies 2 x 4 . For the expression to be defined, x must satisfy both conditions, so x = 2 . Substituting x = 2 into the given equation: ⁻¹(2-1) + ⁻¹(2-3) + ⁻¹ ( 2 2-2^2 ) = ⁻¹ k + ⁻¹(1) + ⁻¹(-1) + ⁻¹ ( 2 -2 ) = ⁻¹ k + 2 + + ⁻¹(-1) = ⁻¹ k + 2 - 4 = ⁻¹ k 4 = ⁻¹ k k = ( 4 ) = 1 2 Answer: 1 2