Find $h(x)$ and $g(x)$ such that $f(x)=(h \circ g)(x)$. \[ f(x)=\sqrt{4 x+4} \] Suppose that $g(x)=4 x+4$.

Step 1 ：Let's find functions $h(x)$ and $g(x)$ such that $f(x)=(h \circ g)(x)$ where $f(x)=\sqrt{4 x+4}$.

Step 2 ：Suppose that $g(x)=4 x+4$.

Step 3 ：To find $h(x)$, we need to express $f(x)$ in terms of $g(x)$. Since $f(x) = \sqrt{4x + 4}$ and $g(x) = 4x + 4$, we can express $f(x)$ as $f(x) = \sqrt{g(x)}$. Therefore, $h(x) = \sqrt{x}$.

Step 4 ：Let's confirm that $h(g(x)) = f(x)$.

Step 5 ：Indeed, substituting $g(x)$ into $h(x)$ gives us $\sqrt{4x + 4}$, which is equal to $f(x)$.

Step 6 ：\(\boxed{h(x) = \sqrt{x}, g(x) = 4x + 4}\) are the correct functions.