To find the inverse function $f^{-1}(x)$ for $f(x) = 2 - x$, we follow these steps:

Step 1: Write the function as $y = f(x)$

$y = 2 - x$

Step 2: Swap $x$ and $y$ to find the inverse

$x = 2 - y$

Step 3: Solve for $y$

Rearranging the equation: $y = 2 - x$

Step 4: Write $f^{-1}(x)$

Thus, the inverse function is: $f^{-1}(x) = 2 - x$

So, the inverse is the same as the original function.

Would you like more details or have any other questions?

Here are 5 related questions to consider:

1. What is the graphical relationship between a function and its inverse?
2. How can you verify that two functions are inverses of each other?
3. What are some real-world examples where inverse functions are useful?
4. How does the domain and range of a function affect its inverse?
5. What is the process for finding the inverse of a quadratic function?

Tip: In general, for linear functions of the form $f(x) = a - x$, the inverse is often a reflection over the line $y = x$.