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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.

If f(x) = 1/x and g(x) = 3x + 2, find g(f(x)).

Learn how to solve the composition of functions problem with f(x) = 1/x and g(x) = 3x + 2. This algebra problem covers key concepts of function composition and simplifies to g(f(x)) = 3/x + 2. Suitable for students in Grades 10-12.

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