For the following two (02) items: Consider the function f(x) = 1 -...

The given function is $f(x) = 1 - \sqrt[3]{(x-1)^2}$.

The expression inside the cube root is $(x-1)^2$, which is a polynomial and is defined for all real values of $x$.

Since the cube root of any real number is well-defined for all real numbers, the function $f(x)$ is defined for all $x \in \mathbb{R}$.

Therefore, the domain of the function is $(-\infty, \infty)$.

Answer: $(-\infty, \infty)$