write the  equation for the inverse function (solved for y). f(x)=0.5x+1

To find the inverse of the function \( f(x) = 0.5x + 1 \), follow these steps:

1. Replace \( f(x) \) with \( y \):
   \[
   y = 0.5x + 1
   \]

2. Swap \( x \) and \( y \) to find the inverse:
   \[
   x = 0.5y + 1
   \]

3. Solve for \( y \) to find the inverse function:
   \[
   x - 1 = 0.5y
   \]
   \[
   y = 2(x - 1)
   \]
   \[
   y = 2x - 2
   \]

So, the equation for the inverse function is:
\[
f^{-1}(x) = 2x - 2
\]

Would you like more details on any step or have any further questions? 

Here are some related questions:

1. How do you verify that two functions are inverses of each other?
2. What is the graphical interpretation of an inverse function?
3. How do you find the inverse of a quadratic function?
4. How do you determine if a function is invertible?
5. How does the domain and range change when finding the inverse of a function?

**Tip:** The graph of a function and its inverse are reflections of each other across the line \( y = x \).

Write the equation for the inverse function (solved for y). f(x) = 0.5x + 1

Discover how to find the inverse of the linear function f(x) = 0.5x + 1. This problem explores key algebraic concepts related to functions and inverse functions, suitable for students in Grades 9-11.

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