Subjects algebra

Inverse Function 31F25B

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1. **State the problem:** We have a one-to-one function $g$ with a vertical asymptote at $x = -5$ and a table of values. We want to find the y-intercept of the inverse function $g^{-1}$ and the equation of the horizontal asymptote of $g^{-1}$. 2. **Recall key facts:** - The y-intercept of $g^{-1}$ is the value of $g^{-1}(0)$, which means the $x$ such that $g(x) = 0$. - The horizontal asymptote of $g^{-1}$ corresponds to the vertical asymptote of $g$ because inverses swap $x$ and $y$. 3. **Find the y-intercept of $g^{-1}$:** From the table, $g(6) = 0$, so $g^{-1}(0) = 6$. Therefore, the y-intercept of $g^{-1}$ is $6$. 4. **Find the horizontal asymptote of $g^{-1}$:** Since $g$ has a vertical asymptote at $x = -5$, the inverse $g^{-1}$ has a horizontal asymptote at $y = -5$. **Final answers:** - The y-intercept of $g^{-1}$ is $6$. - The horizontal asymptote of $g^{-1}$ is $y = -5$.