![\begin{gathered} \text{Given} \\ f(x)=\sqrt[]{x} \\ g(x)=4x+7 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/csjd66b4aglo13u3u9qoies6ccvzv5jrte.png)
Part C: Solving for (f o f)(x)
![\begin{gathered} (f\circ f)(x)=f\Big(f(x)\Big) \\ (f\circ f)(x)=f\Big{(}\sqrt[]{x}\Big{)} \\ (f\circ f)(x)=\sqrt[]{(\sqrt[]{x})} \\ \\ \text{Therefore,} \\ (f\circ f)(x)=\sqrt[4]{x} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/48pk0zat3eybb7rr4qh316z5tg4y5oc6hc.png)
Since the resulting function is a radical function with a even degree (fourth root), we cannot have a negative fourth root, therefore, the domain of the function is

Part D: Solving for (g o g)(x)

Since the resulting function composition is a polynomial (linear function), then the domain of the function is all real numbers.