For $f(x)=4 x-9$ and $g(x)=\frac{1}{4}(x+9)$, find $(f \circ g)(x)$ and $(g \circ f)(x)$. Then determine whether $(f \circ g)(x)=(g \circ f)(x)$. What is $(f \circ g)(x)$ ? \[ (f \circ g)(x)= \]

Step 1 ：Let's find the composition of the functions $f$ and $g$, denoted as $(f \circ g)(x)$, which means that we first apply the function $g$ to $x$, and then apply the function $f$ to the result. In other words, $(f \circ g)(x) = f(g(x))$. To find $(f \circ g)(x)$, we need to substitute $g(x)$ into $f(x)$.

Step 2 ：Given that $f(x) = 4x - 9$ and $g(x) = 0.25x + 2.25$, we substitute $g(x)$ into $f(x)$ to get $f(g(x))$.

Step 3 ：After substitution, we get $f(g(x)) = 4(0.25x + 2.25) - 9$.

Step 4 ：Simplifying the expression, we get $f(g(x)) = x$.

Step 5 ：So, $(f \circ g)(x) = \boxed{x}$.