Use the definition of inverses to determine whether $f$ and $g$ are inverses.
\[
f(x)=-3 x+9, g(x)=-\frac{1}{3} x-9
\]
Are the given functions inverses?
No
Yes

Step 1 ：Given two functions \(f(x)=-3 x+9\) and \(g(x)=-\frac{1}{3} x-9\).

Step 2 ：We need to determine whether these functions are inverses of each other.

Step 3 ：Two functions are inverses of each other if and only if the composition of the two functions in both orders results in the identity function. That is, if \(f(g(x)) = x\) and \(g(f(x)) = x\) for all \(x\) in the domain of the functions.

Step 4 ：Let's substitute \(g(x)\) into \(f(x)\) and \(f(x)\) into \(g(x)\) and simplify.

Step 5 ：For \(f(g(x))\), we get \(x + 36\).

Step 6 ：For \(g(f(x))\), we get \(x - 12\).

Step 7 ：The results of the substitutions are \(x + 36\) and \(x - 12\), not \(x\).

Step 8 ：\(\boxed{\text{Therefore, the functions } f \text{ and } g \text{ are not inverses of each other.}}\)