1. The problem asks to find the domain of the function $$g(x) = \sqrt{7 - x}$$. 2. The domain of a square root function requires the expression inside the root to be non-negative because the square root of a negative number is not a real number. 3. Set the inside of the square root greater than or equal to zero: $$7 - x \geq 0$$ 4. Solve the inequality: $$7 \geq x$$ 5. This means $$x$$ can be any number less than or equal to 7. 6. In interval notation, the domain is: $$(-\infty, 7]$$ Therefore, the domain of $$g(x) = \sqrt{7 - x}$$ is $$(-\infty, 7]$$.