The function provided is $f(x) = \sqrt{x - 1} + \sqrt{x - 3}$, and the task is to find the domain of the function.

Steps to find the domain:

For a square root function to be defined, the expression inside the square root must be non-negative (greater than or equal to zero). This means:

1. $x - 1 \geq 0$, which simplifies to: $x \geq 1$
2. $x - 3 \geq 0$, which simplifies to: $x \geq 3$

To satisfy both conditions, the larger bound (i.e., $x \geq 3$) must be true for both square roots to exist. Therefore, the domain of the function is:

$x \in [3, \infty)$

Final Answer:

The domain of the function is $x \geq 3$ or $[3, \infty)$.

Would you like a detailed explanation or further clarifications?

Here are some related questions you might find useful:

1. What happens to the function if the square roots become undefined?
2. How do we analyze the range of this function given the domain?
3. How do different operations (e.g., addition) between square roots affect the overall domain?
4. Can this method be applied to functions with cube roots?
5. What if there were a third term under the square root?

Tip: Always remember to check all conditions for each square root separately when determining the domain of a function.