Identify $$ f(x) $$ and $$ u=g(x) $$ such that $$ F(x)=f(u)=f(g(x)) $$ for the function $$ F(x)=(7 x-8.2)^{3} $$

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To identify $$ f(x) $$ and $$ u = g(x) $$ such that $$ F(x) = f(u) = f(g(x)) $$ for the function $$ F(x) = (7x - 8.2)^3 $$, we can follow these steps:

1. **Identify the inner function $$ g(x) $$**:
   - The expression $$ (7x - 8.2) $$ is the inner part of the function $$ F(x) $$. Therefore, we can define:
     $$
     g(x) = 7x - 8.2
     $$

2. **Identify the outer function $$ f(u) $$**:
   - The outer function is the cube of the inner function. Thus, we can define:
     $$
     f(u) = u^3
     $$

3. **Combine the definitions**:
   - Now we can express $$ F(x) $$ in terms of $$ f $$ and $$ g $$:
     $$
     F(x) = f(g(x)) = f(7x - 8.2) = (7x - 8.2)^3
     $$

In summary, we have:
- $$ g(x) = 7x - 8.2 $$
- $$ f(u) = u^3 $$

Thus, the functions are:
- $$ f(x) = x^3 $$
- $$ g(x) = 7x - 8.2 $$
$$ f(x) = x^3 $$ and $$ g(x) = 7x - 8.2 $$.

Identify \( f(x) \) and \( u=g(x) \) such that \( F(x)=f(u)=f(g(x)) \) for the function \( F(x)=(7 x-8.2)^{3} \)

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