Consider the following functions.
\[
f(x)=\sqrt{x-2} \text { and } g(x)=\frac{x+5}{3}
\]

Step 2 of 2 : Find the formula for $(g \circ f)(x)$ and simplify your answer. Then find the domain for $(g \circ f)(x)$. Round your answer to two decimal $p$

Step 1 ：Consider the following functions: \(f(x)=\sqrt{x-2}\) and \(g(x)=\frac{x+5}{3}\).

Step 2 ：The function \((g \circ f)(x)\) represents the composition of the functions \(g\) and \(f\), which means we apply the function \(f\) first and then apply the function \(g\) to the result.

Step 3 ：To find the domain of \((g \circ f)(x)\), we need to consider the domain of \(f(x)\) and \(g(x)\). The domain of \(f(x)\) is all \(x\) such that \(x-2 \geq 0\), because we cannot take the square root of a negative number. The domain of \(g(x)\) is all real numbers, because we can divide any real number by 3. Therefore, the domain of \((g \circ f)(x)\) is all \(x\) such that \(x-2 \geq 0\).

Step 4 ：Let's calculate \((g \circ f)(x)\) and its domain. The function \((g \circ f)(x)\) simplifies to \(\frac{\sqrt{x-2}+5}{3}\).

Step 5 ：The domain of \((g \circ f)(x)\) is \(x \geq 2\).

Step 6 ：Final Answer: The formula for \((g \circ f)(x)\) is \(\boxed{\frac{\sqrt{x-2}+5}{3}}\) and the domain for \((g \circ f)(x)\) is \(x \geq 2\). Therefore, the final answer is \(\boxed{\frac{\sqrt{x-2}+5}{3}, x \geq 2}\).