Inverse Function 4C30A0

1. **State the problem:** Find the inverse function $$f^{-1}(x)$$ of the function $$f(x) = 10 - x$$. 2. **Recall the definition of inverse function:** The inverse function $$f^{-1}(x)$$ satisfies $$f(f^{-1}(x)) = x$$. 3. **Start with the equation:** $$y = 10 - x$$. 4. **Swap variables:** Replace $$y$$ with $$x$$ and $$x$$ with $$y$$ to find the inverse: $$x = 10 - y$$. 5. **Solve for $$y$$:** $$y = 10 - x$$. 6. **Therefore, the inverse function is:** $$f^{-1}(x) = 10 - x$$. 7. **Check:** $$f(f^{-1}(x)) = f(10 - x) = 10 - (10 - x) = x$$, confirming the inverse is correct. **Final answer:** $$f^{-1}(x) = 10 - x$$.