Valdez Graham
05/20/2023 · Primary School
Describe the steps involved in finding the inverse of a function algebraically.
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To find the inverse of a function algebraically, follow these steps:
1. **Verify Invertibility:** Ensure the function is one-to-one and onto.
2. **Replace \( f(x) \) with \( y \):** Write \( y = f(x) \).
3. **Swap \( x \) and \( y \):** Change the equation to \( x = f(y) \).
4. **Solve for \( y \):** Isolate \( y \) in terms of \( x \).
5. **Express the Inverse:** Write \( f^{-1}(x) = y \).
6. **Verify the Inverse:** Check that \( f(f^{-1}(x)) = x \) and \( f^{-1}(f(x)) = x \).
By following these steps, you can algebraically determine the inverse of a function.
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