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

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: - \( f(x) = x^3 \) - \( g(x) = 7x - 8.2 \)