1. **State the problem:** We are given two functions: $m(x) = \sqrt{x - 4}$ and $n(x) = x + 1$. We need to find the domain and range of the composition $(m \circ n)(x) = m(n(x))$. 2. **Write the composition:** $$(m \circ n)(x) = m(n(x)) = m(x + 1) = \sqrt{(x + 1) - 4} = \sqrt{x - 3}$$ 3. **Find the domain:** The expression inside the square root must be non-negative: $$x - 3 \geq 0$$ $$x \geq 3$$ So, the domain is all real numbers $x$ such that $x \geq 3$. 4. **Find the range:** Since $m(x) = \sqrt{x - 4}$ outputs values $\geq 0$, and the inside of the root in the composition is $x - 3$ which is $\geq 0$ for $x \geq 3$, the output values are all $y \geq 0$. 5. **Final answer:** - Domain: $[3, \infty)$ - Range: $[0, \infty)$