Find the domain of the function. \[ h(x)=\sqrt{x-1} \] Write your answer as an inequality. Or, you may instead click on "Empty set" or "All reals" as the answer.

Step 1 ：The domain of a function is the set of all possible input values (often the 'x' variable), which produce a valid output from a particular function. For the square root function, the input value should be greater than or equal to 0, because the square root of a negative number is not a real number. So, we need to find the values of x for which the expression under the square root, x-1, is greater than or equal to 0.

Step 2 ：Setting the expression under the square root equal to zero gives us the inequality x-1 >= 0.

Step 3 ：Solving this inequality gives us x >= 1.

Step 4 ：Final Answer: The domain of the function is \(\boxed{x \geq 1}\).