For $f(x)=9x-2$ 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 $(f\circ g)(x)=\boxed{{\displaystyle x}}$, $(g\circ f)(x)=\boxed{{\displaystyle x}}$, $(f\circ g)(9)=\boxed{{\displaystyle 9}}$, and $(g\circ f)(9)=\boxed{{\displaystyle 9}}$.