https://file.aiquickdraw.com/mathbot/file/1729134530783lmfr03mv.jpg

The question displayed in the image is asking to find the inverse function of:

\[
f(x) = \frac{3x + 2}{5}
\]

To find the inverse function, \( f^{-1}(x) \), follow these steps:

1. Replace \( f(x) \) with \( y \):
   \[
   y = \frac{3x + 2}{5}
   \]
   
2. Swap \( x \) and \( y \) to begin solving for the inverse:
   \[
   x = \frac{3y + 2}{5}
   \]

3. Solve for \( y \):
   - Multiply both sides by 5 to get rid of the denominator:
     \[
     5x = 3y + 2
     \]
   - Subtract 2 from both sides:
     \[
     5x - 2 = 3y
     \]
   - Divide both sides by 3:
     \[
     y = \frac{5x - 2}{3}
     \]

4. Therefore, the inverse function is:
   \[
   f^{-1}(x) = \frac{5x - 2}{3}
   \]

Would you like any further explanation on these steps?

Here are five related questions to expand your understanding:
1. What is the inverse of the function \( f(x) = \frac{2x - 1}{4} \)?
2. How do you verify if two functions are inverses of each other?
3. Can every function have an inverse? Why or why not?
4. How do the domain and range change when finding the inverse of a function?
5. What are some real-world applications of inverse functions?

**Tip:** Always check if a function is one-to-one before finding its inverse to ensure it exists.

Find the inverse function of f(x) = (3x + 2) / 5

Learn how to find the inverse function of f(x) = (3x + 2) / 5 using algebraic methods. This step-by-step guide covers key concepts related to inverse functions and linear equations, suitable for students in Grades 9-12.

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