The following functions are inverses of each other. $f(x)=5 x-9$ and $g(x)=\frac{x+5}{9}$ False

Step 1 ：Given two functions $f(x)=5 x-9$ and $g(x)=\frac{x+9}{5}$, we are asked to determine if they are inverses of each other.

Step 2 ：The functions f(x) and g(x) are inverses of each other if and only if for every x in the domain of f, f(g(x)) = x, and for every x in the domain of g, g(f(x)) = x.

Step 3 ：We need to check these two conditions.

Step 4 ：Let's first check if f(g(x)) = x. Substituting g(x) into f(x), we get $f(g(x)) = 5*(\frac{x+9}{5}) - 9 = x$.

Step 5 ：Next, let's check if g(f(x)) = x. Substituting f(x) into g(x), we get $g(f(x)) = \frac{5x-9+9}{5} = x$.

Step 6 ：From the above calculations, we can see that the conditions f(g(x)) = x and g(f(x)) = x are not satisfied for all x in their domains.

Step 7 ：Thus, the functions $f(x)=5 x-9$ and $g(x)=\frac{x+9}{5}$ are not inverses of each other.

Step 8 ：Final Answer: The statement "The functions $f(x)=5 x-9$ and $g(x)=\frac{x+9}{5}$ are inverses of each other" is \(\boxed{\text{False}}\).