For $f(x)=9 x-2$ and $g(x)=\frac{x+2}{9}$, find the following functions.
a. $(f \circ g)(x) ;$ b. $(g \circ f)(x) ;$ c. $(f \circ g)(9) ;$ d. $(g \circ f)(9)$
a. $(f \circ g)(x)=$
(Simplify your answer.)
b. $(g \circ f)(x)=$
(Simplify your answer.)
c. $(f \circ g)(9)=$
d. $(g \circ f)(9)=$

Step 1 ：First, we find the composition of the functions $f$ and $g$, denoted as $(f \circ g)(x)$, which means we substitute $g(x)$ into $f(x)$.

Step 2 ：Substitute $g(x)$ into $f(x)$, we get $f(g(x)) = f\left(\frac{x+2}{9}\right) = 9\left(\frac{x+2}{9}\right) - 2$.

Step 3 ：Simplify the above expression, we get $f(g(x)) = x + 2 - 2 = x$.

Step 4 ：Next, we find the composition of the functions $g$ and $f$, denoted as $(g \circ f)(x)$, which means we substitute $f(x)$ into $g(x)$.

Step 5 ：Substitute $f(x)$ into $g(x)$, we get $g(f(x)) = g(9x-2) = \frac{9x-2+2}{9}$.

Step 6 ：Simplify the above expression, we get $g(f(x)) = x$.

Step 7 ：Then, we find the value of $(f \circ g)(9)$, which means we substitute $9$ into $f(g(x))$.

Step 8 ：Substitute $9$ into $f(g(x))$, we get $f(g(9)) = 9$.

Step 9 ：Finally, we find the value of $(g \circ f)(9)$, which means we substitute $9$ into $g(f(x))$.

Step 10 ：Substitute $9$ into $g(f(x))$, we get $g(f(9)) = 9$.

Step 11 ：So, the final answers are $(f \circ g)(x) = \boxed{x}$, $(g \circ f)(x) = \boxed{x}$, $(f \circ g)(9) = \boxed{9}$, and $(g \circ f)(9) = \boxed{9}$.