To find the inverse function of $f(x) = 4 - x$, follow these steps:

1. Replace $f(x)$ with $y$: $y = 4 - x$

2. Swap $x$ and $y$ to prepare for finding the inverse: $x = 4 - y$

3. Solve for $y$: $y = 4 - x$

4. Rename $y$ as $f^{-1}(x)$: $f^{-1}(x) = 4 - x$

Final Answer:

The inverse of $f(x) = 4 - x$ is: $f^{-1}(x) = 4 - x$

Explanation:

This result shows that $f(x)$ is self-inverse, meaning that $f(f(x)) = x$.

Let me know if you'd like further clarification or examples of verifying inverse functions! 😊

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Related Questions:

1. How do you verify if a function and its inverse are correct?
2. Can you give an example of a self-inverse function besides this one?
3. What are the necessary conditions for a function to have an inverse?
4. How do you graph a function and its inverse on the same plot?
5. What happens to the domain and range when a function is inverted?

Tip:

When finding inverses, always ensure the original function is one-to-one (passes the horizontal line test). This guarantees it has an inverse!