1. **State the problem:** Find the domain of the function $$f(x) = \sqrt[3]{x+3}$$. 2. **Recall the domain rules for cube roots:** The cube root function $$\sqrt[3]{x}$$ is defined for all real numbers because you can take the cube root of any real number, including negatives. 3. **Apply the rule to the function:** Since $$f(x) = \sqrt[3]{x+3}$$ involves a cube root, the expression inside the root, $$x+3$$, can be any real number. 4. **Write the domain:** Therefore, the domain is all real numbers, which can be written as $$(-\infty, \infty)$$. **Final answer:** The domain of $$f(x) = \sqrt[3]{x+3}$$ is all real numbers, $$\boxed{(-\infty, \infty)}$$.