To find the function $g(f(x))$, we need to substitute $f(x)$ into the function $g(x)$.

Given: $f(x) = \frac{x}{x - 7}$ $g(x) = \frac{3}{x}$

We substitute $f(x)$ into $g(x)$:

$g(f(x)) = g\left(\frac{x}{x - 7}\right)$

Now, replace $x$ in $g(x)$ with $\frac{x}{x - 7}$:

$g(f(x)) = \frac{3}{\frac{x}{x - 7}}$

Next, simplify the expression:

$g(f(x)) = \frac{3 \cdot (x - 7)}{x}$

Distribute the 3 in the numerator:

$g(f(x)) = \frac{3x - 21}{x}$

Simplify further:

$g(f(x)) = 3 - \frac{21}{x}$

So, the function $g(f(x))$ is:

$g(f(x)) = 3 - \frac{21}{x}$

Would you like more details or have any questions about this process?

Here are some related questions:

1. How do you find the domain of $g(f(x))$?
2. What is $f(g(x))$?
3. How do you determine the inverse of $g(x)$?
4. What is the value of $g(f(7))$?
5. How would you graph $g(f(x))$?

Tip: When working with composite functions, always check for simplifications that might make the function easier to understand or work with.