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 $y = x$.