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From the image you uploaded, I can make out the following information:

It states:

1. Given functions \( f(x) = \frac{2}{3x} \) and \( g(x) = 3x - 1 \),
2. Find \( f^{-1}(x) \) (the inverse of \( f(x) \)).

Let's go step-by-step to solve the problem:

### Finding the inverse of \( f(x) = \frac{2}{3x} \):

1. **Rewrite \( f(x) \) as \( y = \frac{2}{3x} \).**
   \[
   y = \frac{2}{3x}
   \]

2. **Swap \( x \) and \( y \) to begin the process of finding the inverse:**
   \[
   x = \frac{2}{3y}
   \]

3. **Solve for \( y \):**
   Multiply both sides by \( 3y \):
   \[
   3xy = 2
   \]
   Then, divide both sides by \( 3x \):
   \[
   y = \frac{2}{3x}
   \]

4. Therefore, the inverse function \( f^{-1}(x) \) is:
   \[
   f^{-1}(x) = \frac{2}{3x}
   \]

### Do you have any specific questions, or would you like to explore further?

Here are 5 questions that might help you expand your understanding:
1. How do you find the inverse of more complex functions?
2. What is the geometric meaning of an inverse function?
3. How do you verify if two functions are inverses of each other?
4. How does the domain and range change when finding the inverse of a function?
5. How do composition of functions work with inverse functions?

**Tip:** Always check the domain of the original function when finding its inverse!

Given functions f(x) = 2/3x and g(x) = 3x - 1, find the inverse function f⁻¹(x).

Learn how to find the inverse of the function f(x) = 2/(3x) with a step-by-step solution. This problem explores the concepts of functions, inverse functions, and algebra, suitable for high school students in Grades 10-12.

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