Perform the indicated operation.
If $f(x)=\log _{9} x$, find the following values.
(a) $f(\sqrt{9})$
(b) $f(0)$

Select the correct choice below, and, if necessary, fill in th
A. $f(\sqrt{9})=\square$ (Type an integer or a fraction.)
B. $f(\sqrt{9})$ is not defined.

Step 1 ：The function \(f(x)=\log _{9} x\) is a logarithmic function with base 9. To find the value of \(f(\sqrt{9})\), we need to substitute \(\sqrt{9}\) into the function.

Step 2 ：The square root of 9 is 3, so we are essentially finding the logarithm base 9 of 3. In other words, we are trying to find a number that, when 9 is raised to that power, gives us 3.

Step 3 ：The result of the calculation is 0.5. This means that \(f(\sqrt{9})=0.5\). This makes sense because \(9^{0.5}=3\), which is the value we substituted into the function.

Step 4 ：Now, let's move on to the second part of the question, which is to find \(f(0)\). However, we should note that the logarithm of 0 is undefined because there is no exponent you can raise to 9 to get 0. Therefore, \(f(0)\) is not defined.

Step 5 ：Final Answer: \n(a) \(f(\sqrt{9})=\boxed{0.5}\)\n(b) \(f(0)\) is not defined.