What is the inverse of the function f(x) = 2x – 10?

To find the inverse of the function \( f(x) = 2x - 10 \), follow these steps:

### Steps:
1. Replace \( f(x) \) with \( y \):
   \[
   y = 2x - 10
   \]
   
2. Swap \( x \) and \( y \) to solve for the inverse:
   \[
   x = 2y - 10
   \]

3. Solve for \( y \) (the inverse function):
   \[
   x + 10 = 2y
   \]
   \[
   y = \frac{x + 10}{2}
   \]

Thus, the inverse function is:
\[
f^{-1}(x) = \frac{x + 10}{2}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How can we verify that two functions are inverses of each other?
2. What is the domain and range of the inverse function?
3. How would the graph of a function and its inverse look like?
4. What are the properties of inverse functions in general?
5. Can every function have an inverse?

**Tip:** The graph of a function and its inverse are symmetric about the line \( y = x \).

Learn how to find the inverse of the linear function f(x) = 2x - 10 with step-by-step instructions. This problem covers important algebraic concepts related to inverse functions and linear equations. Suitable for students in Grades 9-11.

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