What is the domain and range of  y= sqrt(x-1)?

Domain is $x \ge 1$. Range is all real numbers.
Note that $\left(x - 1\right)$ cannot take negative values of $y$ is real. Assuming that we are working in real number domain, it is obvious x cannot take values less than one. Hence, domain is $x \ge 1$.
However, as $\sqrt{x - 1}$, $y$ can take any value. Hencr, range is all real numbers.