b) $f(x)=\ln (9 x-7)$ Domain:

Step 1 ：The function is given as \(f(x)=\ln (9 x-7)\).

Step 2 ：The domain of a function is the set of all possible input values (x-values) which will output real numbers.

Step 3 ：For the function \(f(x)=\ln (9 x-7)\), the argument of the logarithm, \((9x - 7)\), must be greater than zero for the function to output real numbers.

Step 4 ：Therefore, we need to solve the inequality \(9x - 7 > 0\) to find the domain of the function.

Step 5 ：Solving the inequality gives us \(x > \frac{7}{9}\).

Step 6 ：Final Answer: The domain of the function \(f(x)=\ln (9 x-7)\) is \(\boxed{x > \frac{7}{9}}\).