1. **State the problem:** We need to find the values of the function $g(x) = \sqrt{(y - 1)(y - 2)}$ at $x = 2$, $x = 0$, and $x = 4$. However, the function is given in terms of $y$, so we assume $y = x$ for evaluation. 2. **Recall the function:** $$g(x) = \sqrt{(x - 1)(x - 2)}$$ 3. **Evaluate $g(2)$:** $$g(2) = \sqrt{(2 - 1)(2 - 2)} = \sqrt{1 \times 0} = \sqrt{0} = 0$$ 4. **Evaluate $g(0)$:** $$g(0) = \sqrt{(0 - 1)(0 - 2)} = \sqrt{(-1)(-2)} = \sqrt{2}$$ 5. **Evaluate $g(4)$:** $$g(4) = \sqrt{(4 - 1)(4 - 2)} = \sqrt{3 \times 2} = \sqrt{6}$$ 6. **Final answers:** $$g(2) = 0, \quad g(0) = \sqrt{2}, \quad g(4) = \sqrt{6}$$