1. **State the problem:** We need to find the expression for $k(x) - h(x)$ where $k(x) = \sqrt{x+3}$ and $h(x) = x^3 + 4$. 2. **Write the expression:** $$k(x) - h(x) = \sqrt{x+3} - (x^3 + 4)$$ 3. **Simplify the expression:** $$k(x) - h(x) = \sqrt{x+3} - x^3 - 4$$ 4. **Explain the domain:** The square root function $\sqrt{x+3}$ requires $x+3 \geq 0$, so $x \geq -3$. 5. **Summary:** The function $k(x) - h(x)$ is $$k(x) - h(x) = \sqrt{x+3} - x^3 - 4$$ valid for $x \geq -3$. This expression represents the difference between the two given functions.