Domain of the Function:
The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. In this case, we have the function f(x) = √(x-1).

To determine the domain, we need to identify any restrictions on the values of x that would make the function undefined. In this case, the function involves taking the square root of (x-1), so the expression inside the square root must be non-negative. In other words, (x-1) ≥ 0.

To find the domain, we solve the inequality:
x - 1 ≥ 0

Simplifying the inequality, we get:
x ≥ 1

Therefore, the domain of the function f(x) = √(x-1) is all real numbers greater than or equal to 1.

Range of the Function:
The range of a function refers to the set of all possible output values (y-values) that the function can produce.

In this case, the function f(x) = √(x-1) involves taking the square root of (x-1). The square root function outputs non-negative values, which means the range of the function is all real numbers greater than or equal to 0.

To illustrate this, consider the function evaluated for different input values:
- For x = 1, f(1) = √(1-1) = √0 = 0.
- For x > 1, the expression (x-1) is positive, so the square root of a positive number is always non-negative.

Based on these evaluations, we can conclude that the range of the function f(x) = √(x-1) is all real numbers greater than or equal to 0.

Summary:
- The domain of the function f(x) = √(x-1) is all real numbers greater than or equal to 1.
- The range of the function is all real numbers greater than or equal to 0.