Question 2 of 12, Step 1 of 2 $1 / 18$ Correct Consider the following functions. \[ f(x)=\frac{1}{x} \text { and } g(x)=\frac{x-4}{5} \] Step 1 of 2 : Find the formula for $(f \circ g)(x)$ and simplify your answer. Then find the domain for $(f \circ g)(x)$. Round your answer to two decimal places, if necessary. Answer Keypad

Step 1 ：The function $(f \circ g)(x)$ represents the composition of the functions $f$ and $g$, which means we apply the function $g$ first and then apply the function $f$ to the result. The formula for $(f \circ g)(x)$ is therefore $f(g(x))$.

Step 2 ：To find the domain of $(f \circ g)(x)$, we need to consider the domain of $g(x)$ and the range of $g(x)$ that is within the domain of $f(x)$. The domain of $g(x)$ is all real numbers, because $g(x)$ is a linear function. The domain of $f(x)$ is all real numbers except 0, because $f(x)$ is a reciprocal function. Therefore, the domain of $(f \circ g)(x)$ is all real numbers except the value of $x$ that makes $g(x) = 0$.

Step 3 ：The formula for $(f \circ g)(x)$ is $f(g(x)) = \frac{1}{\frac{x-4}{5}} = \frac{5}{x-4}$. The domain of $(f \circ g)(x)$ is all real numbers except $x = 4$, because $g(4) = 0$ and $f(x)$ is undefined at $x = 0$.

Step 4 ：Final Answer: The formula for $(f \circ g)(x)$ is $\boxed{\frac{5}{x-4}}$ and the domain is all real numbers except $\boxed{4}$.