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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 \( y = x \).

Let f(x) = 2 - x. Find the inverse function f^{-1}(x).

Learn how to find the inverse of the linear function f(x) = 2 - x. This problem involves key algebraic concepts such as inverse functions, solving equations, and swapping variables. Suitable for students in Grades 8-10.

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