The function $g(x) = (2x+1)^4$ is a composite function because it can be expressed as the composition of two simpler functions.

To identify the "inner" and "outer" functions, consider the following:

1. The "inner" function is the part of the expression that is inside another function. Here, the expression inside the fourth power is $2x+1$.
2. The "outer" function is the function that applies to the result of the "inner" function. In this case, we take the fourth power of whatever is inside, so the outer function is $x^4$.

Thus, we have:

• The "inner" function $u(x) = 2x+1$
• The "outer" function $w(x) = x^4$

This matches the description in Choice B.

Correct Answer: B: $g$ is composite. The "inner" function is $2x+1$ and the "outer" function is $x^4$.

Would you like more details or have any questions? Here are 5 related questions to expand your understanding:

1. How do you determine the derivative of a composite function using the chain rule?
2. Can you provide an example of a different composite function with a polynomial as the outer function?
3. What are some common examples of composite functions in real-life applications?
4. Why is understanding the structure of a composite function important in calculus?
5. How can you determine if a function is composite just by looking at its expression?

Tip: The "inner" function is usually the expression directly affecting the variable $x$, and the "outer" function is what is applied to that result.