1. The problem asks for the domain of the function $f(x) = \sqrt{x - 4}$.\n\n2. The domain of a square root function is all values of $x$ for which the expression inside the square root is non-negative because the square root of a negative number is not a real number.\n\n3. Set the inside of the square root greater than or equal to zero: $$x - 4 \geq 0$$\n\n4. Solve the inequality: $$x \geq 4$$\n\n5. This means the domain includes all real numbers $x$ such that $x$ is greater than or equal to 4.\n\n6. Therefore, the correct answer is option B: $x \geq 4$.