1. The problem asks for the function of $g^n(x)$ in terms of $n$ and $x$. 2. Here, $g^n(x)$ denotes the $n$-th iterate of the function $g$, meaning applying $g$ to $x$ repeatedly $n$ times. 3. The general formula for the $n$-th iterate is: $$g^n(x) = \underbrace{g(g(\cdots g}_{n\text{ times}}(x)\cdots))$$ 4. To express $g^n(x)$ explicitly, we need the definition of $g(x)$. 5. Without a specific form of $g(x)$, we cannot simplify further. 6. If $g(x)$ is known, substitute and simplify iteratively or find a closed form if possible. Final answer: $g^n(x)$ is the $n$-fold composition of $g$ applied to $x$, i.e., $g^n(x) = g(g^{n-1}(x))$ with $g^0(x) = x$.