The function $f$ is defined by $f(x)=\frac{4+x}{5+4 x}$. Find $f(3 x)$ \[ f(3 x)= \]

Step 1 ：The function $f$ is defined by $f(x)=\frac{4+x}{5+4 x}$.

Step 2 ：We are asked to find the value of the function $f(x)$ when $x$ is replaced by $3x$.

Step 3 ：Substitute $3x$ into the function $f(x)$ to get $f(3x)$.

Step 4 ：So, $f(3x) = \frac{4+3x}{5+12x}$.

Step 5 ：\(\boxed{f(3x) = \frac{3x + 4}{12x + 5}}\)