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The problem asks to find the inverse of the function \( f(x) = 10x + 6 \).

To find the inverse, follow these steps:

1. Start with the given function:
   \[
   f(x) = 10x + 6
   \]

2. Replace \( f(x) \) with \( y \):
   \[
   y = 10x + 6
   \]

3. Swap \( x \) and \( y \) to solve for the inverse:
   \[
   x = 10y + 6
   \]

4. Solve for \( y \):
   \[
   x - 6 = 10y
   \]
   \[
   y = \frac{x - 6}{10}
   \]

So, the inverse function is:
\[
f^{-1}(x) = \frac{x - 6}{10}
\]

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

Here are 5 related questions you might find interesting:
1. How do you find the inverse of a quadratic function?
2. Can every function have an inverse?
3. How can you verify if two functions are inverses of each other?
4. What are the graphical interpretations of a function and its inverse?
5. How does the concept of an inverse function apply in real-world situations?

**Tip**: To verify that two functions are inverses, check if \( f(f^{-1}(x)) = x \) and \( f^{-1}(f(x)) = x \).

Learn how to find the inverse of the linear function f(x) = 10x + 6. This step-by-step solution covers key algebraic concepts such as inverse functions and solving linear equations. Suitable for high school students in Grades 9-12.

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