We are given two functions $f(x) = \frac{1}{x}$ and $g(x) = 3x + 2$, and we are asked to find $g(f(x))$.

To solve this:

1. We first find $f(x)$, which is $\frac{1}{x}$.
2. Now, substitute $f(x)$ into $g(x)$ where $x$ appears. So: $g(f(x)) = g\left( \frac{1}{x} \right) = 3\left( \frac{1}{x} \right) + 2$ Simplifying this: $g(f(x)) = \frac{3}{x} + 2$

This matches option B.

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

Here are 5 related questions to explore:

1. How would the solution change if $f(x) = \frac{2}{x}$?
2. Can you solve for $g(f(x))$ if $g(x) = x^2 + 1$?
3. What happens if $f(x)$ is a polynomial function?
4. How do we solve for $g(f(x))$ when both functions are rational functions?
5. How does composing functions like this relate to the chain rule in calculus?

Tip: When composing functions, always substitute one function's output where the other function expects an input.