The domain of the function f(x) = ⁻¹( x - 1 )

Step-by-step solution

For the function f(x) = ⁻¹( x - 1 ) to be defined, the argument of the inverse sine function must lie in the interval [-1, 1] . -1 x - 1 1 Since the principal square root is always non-negative, this inequality reduces to: 0 x - 1 1 Squaring all parts of the inequality, we get: 0 x - 1 1 Adding 1 to all parts, we obtain: 1 x 2 Thus, the domain of the function is [1, 2] . Answer: [1, 2]