Bob Murray
05/15/2024 · High School
nd the inverse function of \( f(x) \). State the domain of the inverse function \( f^{-1}(x) \)
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Step-by-step Solution
To find the inverse function \( f^{-1}(x) \) of a given function \( f(x) \), we typically follow these steps:
1. **Replace \( f(x) \) with \( y \)**: Start by writing the equation as \( y = f(x) \).
2. **Solve for \( x \)**: Rearrange the equation to express \( x \) in terms of \( y \).
3. **Swap \( x \) and \( y \)**: Once you have \( x \) in terms of \( y \), swap the variables to get the inverse function \( y = f^{-1}(x) \).
4. **Determine the domain of the inverse function**: The domain of \( f^{-1}(x) \) is the range of the original function \( f(x) \).
Since you haven't provided a specific function \( f(x) \), I can't perform these steps directly. If you provide the function, I can help you find its inverse and state the domain of the inverse function.
Quick Answer
To find the inverse function, replace \( f(x) \) with \( y \), solve for \( x \), swap \( x \) and \( y \), and the domain of the inverse is the range of the original function.
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