The function in the image is $f(x) = \sqrt{x - 1}$.

To find the domain, we need to determine the values of $x$ for which the function is defined. The square root function is only defined for non-negative values of the expression inside the radical, which means we need:

$x - 1 \geq 0$

Solving this inequality:

$x \geq 1$

Thus, the domain of the function is $x \geq 1$, or in interval notation, the domain is:

$[1, \infty)$

Let me know if you'd like further clarification on this or if you have any other questions!

Here are 5 follow-up questions related to this topic:

1. What is the range of the function $f(x) = \sqrt{x - 1}$?
2. How do we find the domain of a rational function?
3. What happens to the function $f(x) = \sqrt{x - 1}$ when $x < 1$?
4. How would you graph the function $f(x) = \sqrt{x - 1}$?
5. Can you explain how to solve similar domain problems for other functions like $f(x) = \sqrt{x^2 - 4}$?

Tip: When dealing with square roots, remember the expression under the square root must be non-negative, as the square root of a negative number is not a real number.