To decompose the function \( f(x) = x^3 \), you can express it as a composition of simpler functions. One common way is:

1. **Outer function** \( g(u) \): Let \( g(u) = u^3 \).
2. **Inner function** \( h(x) \): Let \( h(x) = x \).

Then, the function \( f(x) = x^3 \) can be written as:

\[ f(x) = g(h(x)) \]

Here’s the breakdown:

- Start with the inner function \( h(x) = x \).
- Apply the outer function \( g(u) = u^3 \) to \( h(x) \).

So, \( f(x) = g(h(x)) = (x)^3 \).

### Verification:

\[ f(x) = g(h(x)) = g(x) = x^3 \]

This shows that the composition of the functions \( g \) and \( h \)

Discover how to decompose the function f(x) = x³ into simpler functions with this step-by-step guide. Explore the concept of function decomposition and the composition of functions. Suitable for advanced high school students and college-level learners.

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