Bryant Campbell
09/22/2023 · Middle School
The one-to-one function \( f \) is defined below. \[ f(x)=\frac{8 x-9}{7 x+8} \] Find \( f^{-1}(x) \), where \( f^{-1} \) is the inverse of \( f \). Also state the domain and range of \( f^{-1} \) in interval notation.
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The inverse function \( f^{-1}(x) \) is \( f^{-1}(x) = \frac{-9 - 8x}{7x - 8} \). The domain of \( f^{-1}(x) \) is \( (-\infty, -\frac{8}{7}) \cup (-\frac{8}{7}, \infty) \), and the range is \( (-\infty, \frac{8}{7}) \cup (\frac{8}{7}, \infty) \).
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