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:

1. Replace \( f(x) \) with \( y \):  
   \[
   y = 2x - 10
   \]

2. Swap \( x \) and \( y \) (this is how we find the inverse):  
   \[
   x = 2y - 10
   \]

3. Solve for \( y \):

   \[
   x + 10 = 2y
   \]
   \[
   y = \frac{x + 10}{2}
   \]

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

Would you like a more detailed explanation or have any further questions?

Here are some related questions:
1. How do you verify if two functions are inverses of each other?
2. What is the graphical relationship between a function and its inverse?
3. How would the inverse change if the original function was \( f(x) = 3x - 10 \)?
4. What happens to the inverse function if you add a constant to \( f(x) \)?
5. How do you find the inverse of more complex functions, such as quadratic functions?

**Tip**: A function's inverse reflects the original function across the line \( y = x \).

This guide explains how to find the inverse of the linear function f(x) = 2x - 10. Learn the step-by-step process, including key algebraic concepts, such as swapping variables and solving for y. Suitable for students in Grades 9-11.

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