Question: Find two functions, $f(x)$ and $g(x)$, so that $F(x)=(f\circ g)(x)$. Enter your answers as a comma-separated list. $F(x) = (x - 6)^6$ $(f(x), g(x)) =$
1. **State the problem:** We need to find two functions $f(x)$ and $g(x)$ such that their composition $F(x) = (f \circ g)(x)$ equals $(x - 6)^6$.
2. **Recall the composition definition:** The composition $(f \circ g)(x)$ means $f(g(x))$.
3. **Analyze the given function:** $F(x) = (x - 6)^6$ can be seen as a function raised to the 6th power.
4. **Choose inner function $g(x)$:** Let $g(x) = x - 6$.
5. **Choose outer function $f(x)$:** Since $F(x) = (g(x))^6$, let $f(x) = x^6$.
6. **Verify the composition:**
$$
(f \circ g)(x) = f(g(x)) = (x - 6)^6 = F(x)
$$
7. **Final answer:**
$$(f(x), g(x)) = (x^6, x - 6)$$