1. The problem is to find the domain of the function $f(x) = \sqrt{x} - 4$. 2. The domain of a function is the set of all input values ($x$) for which the function is defined. 3. For the square root function $\sqrt{x}$, the expression inside the root must be greater than or equal to zero because the square root of a negative number is not a real number. 4. Therefore, we set the inequality: $$x \geq 0$$ 5. This means $x$ can be any real number greater than or equal to zero. 6. The function $f(x) = \sqrt{x} - 4$ is defined for all $x$ such that $x \geq 0$. 7. Hence, the domain of $f(x)$ is: $$[0, \infty)$$