The function h(x)=(x+4)$$ ^3 $$can be expressed in the form f(g(x)), where f(x)=$$ x^3 $$, and g(x) is defined below:

g(x) = 

The function $ h(x) = (x + 4)^3 $ can be expressed in the form $ f(g(x)) $ where $ f(x) = x^3 $.

To express $ h(x) $ in this form:

1. We are given $ f(x) = x^3 $.
2. Then, we express $ h(x) = (x + 4)^3 $ by identifying the inner function $ g(x) $ such that $ g(x) = x + 4 $.

So, the function $ g(x) $ is defined as:
\[ g(x) = x + 4 \]

Would you like further details or have any questions?

Here are 5 related questions:
1. How can you verify that $ h(x) = f(g(x)) $ using the functions provided?
2. What is the inverse of the function $ g(x) = x + 4 $?
3. How does the function $ f(x) = x^3 $ affect the graph of $ g(x) = x + 4 $?
4. Can you express $ h(x) $ using a different pair of functions $ f(x) $ and $ g(x) $?
5. What is the derivative of $ h(x) = (x + 4)^3 $ using the chain rule?

**Tip:** When decomposing functions into $ f(g(x)) $, identify how the given function is transformed and map those transformations to the appropriate inner and outer functions.

Explore how to express the function h(x) = (x + 4)^3 in the form f(g(x)) using specific mathematical transformations. Learn about the composition of functions and the application of the chain rule in derivatives. Suitable for advanced high school students.

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