Let h(x) = sin⁻¹(x - 3) + sin⁻¹(5 - x). Find the domain of h…

Step 1. The first condition. $-1 \le x - 3 \le 1$ gives $2 \le x \le 4$.

Step 2. The second condition. $-1 \le 5 - x \le 1$ gives $4 \le x \le 6$.

Step 3. The overlap. The two intervals share only $x = 4$. So the domain has exactly one number.

Step 4. The value. $h(4) = \sin^{-1}1 + \sin^{-1}1 = \dfrac{\pi}{2} + \dfrac{\pi}{2} = \pi = 3.1416$.