Chapter 7 - Analytic Trigonometry - 7.1 The Inverse Sine, Cosine, and Tangent Functions - 7.1 Assess Your Understanding - Page 450: 2

$x\le1$ or $x\ge1$.

We can see that $f(x)=(x-1)^2$ is symmetric with respect to $x=1$. To form a one-to-one function, we can select the left or right part separated by $x=1$. Thus the restriction could be $x\le1$ or $x\ge1$.