To find the inverse of the function \( f(x) = 2x - 7 \), we follow these steps:
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Replace \( f(x) \) with \( y \): \[ y = 2x - 7 \]
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Swap \( x \) and \( y \): \[ x = 2y - 7 \]
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Solve for \( y \):
- Add 7 to both sides: \[ x + 7 = 2y \]
- Divide by 2: \[ y = \frac{x + 7}{2} \]
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Replace \( y \) with \( f^{-1}(x) \): \[ f^{-1}(x) = \frac{x + 7}{2} \]
So, the inverse of the function \( f(x) = 2x - 7 \) is: \[ f^{-1}(x) = \frac{x + 7}{2} \]