Find the domain of the function.
\[
f(x)=\ln (7-2 x)
\]
Write your answer as an interval or union of intervals.
Final Answer: The domain of the function is \(\boxed{(-\infty, \frac{7}{2})}\).
Step 1 :The domain of a function is the set of all possible input values (x-values) which will produce a valid output.
Step 2 :For the function \(f(x) = \ln(7-2x)\), the argument of the logarithm (7-2x) must be greater than zero, because the logarithm of a non-positive number is undefined.
Step 3 :Therefore, we need to solve the inequality 7-2x > 0 to find the domain of the function.
Step 4 :The solution to the inequality 7-2x > 0 is x < 7/2.
Step 5 :This means that the domain of the function \(f(x) = \ln(7-2x)\) is all real numbers less than 7/2.
Step 6 :Final Answer: The domain of the function is \(\boxed{(-\infty, \frac{7}{2})}\).