The function given is $f(x) = \sqrt[3]{x+4}$, which is a cube root function.

Domain Analysis:

• Cube roots, unlike square roots, can accept both positive and negative values as inputs.
• The cube root function $\sqrt[3]{x}$ is defined for all real numbers $x$, meaning there are no restrictions on the input.

Thus, the function $\sqrt[3]{x+4}$ is defined for all real values of $x$, because there are no values of $x$ that would make the expression inside the cube root undefined.

Domain:

The domain of $f(x) = \sqrt[3]{x+4}$ is: $\boxed{(-\infty, \infty)}$

Would you like any further explanation on cube roots or domains?

Here are 5 related questions:

1. What is the domain of $\sqrt{2x - 5}$?
2. What is the range of $f(x) = \sqrt[3]{x+4}$?
3. How would the domain change for $f(x) = \sqrt{x+4}$?
4. What is the graph of $f(x) = \sqrt[3]{x+4}$ like?
5. How do cube roots differ from square roots in terms of their domain and range?

Tip: Cube root functions are always defined for all real numbers, while square root functions are only defined for non-negative numbers under the square root.