\[
f(x)=\frac{1}{x} \text { and } g(x)=\frac{x-4}{5}
\]
$(f \circ g)(x)$ and simplify your answer. Then find the domain for $(f \circ g)(x)$. Round your answer to two decimal pl.
Answer
The simplified form of \(f(g(x))\) is \(\boxed{\frac{5}{x - 4}}\) and the domain is all real numbers except 4, so the final answer is \(\boxed{\frac{5}{x - 4}}\) and \(\boxed{x \neq 4}\).
Step 1 ：Define the functions \(f(x) = \frac{1}{x}\) and \(g(x) = \frac{x-4}{5}\).
Step 2 ：Find the composition of the functions, which is \(f(g(x))\).
Step 3 ：Simplify the composition of the functions to get \(f(g(x)) = \frac{5}{x - 4}\).
Step 4 ：Find the domain of the function by setting the denominator equal to zero and solving for x, which gives \(x \neq 4\).
Step 5 ：The simplified form of \(f(g(x))\) is \(\boxed{\frac{5}{x - 4}}\) and the domain is all real numbers except 4, so the final answer is \(\boxed{\frac{5}{x - 4}}\) and \(\boxed{x \neq 4}\).
