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 $(f \circ g)(x) ?$ \[ (f \circ g)(x)=x \] What is $(g \circ f)(x)$ ? \[ (g \circ f)(x)= \]

Step 1 ：Given functions are $f(x)=4 x-9$ and $g(x)=\frac{1}{4}(x+9)$.

Step 2 ：To find $(f \circ g)(x)$, substitute $g(x)$ into $f(x)$: $f(g(x))=4(\frac{1}{4}(x+9))-9=x$.

Step 3 ：To find $(g \circ f)(x)$, substitute $f(x)$ into $g(x)$: $g(f(x))=\frac{1}{4}(4x-9+9)=x$.

Step 4 ：Comparing the two results, we find that $(f \circ g)(x)=(g \circ f)(x)$.

Step 5 ：Final Answer: \(\boxed{x}\)