1. **State the problem:** We are given the inverse function $f^{-1}(x)$ as a set of points: $\{(1, -10), (-5, -8), (10, -7), (0, -6), (6, 0)\}$. We want to understand the domain and range of the original function $f(x)$ based on this information. 2. **Recall the relationship between a function and its inverse:** The inverse function $f^{-1}(x)$ swaps the roles of inputs and outputs of $f(x)$. That means if $f(a) = b$, then $f^{-1}(b) = a$. 3. **Identify the domain and range of $f^{-1}(x)$:** - Domain of $f^{-1}$ is the set of all $x$-values in the inverse function points: $\{-10, -8, -7, -6, 0\}$. - Range of $f^{-1}$ is the set of all $y$-values in the inverse function points: $\{1, -5, 10, 0, 6\}$. 4. **Find the domain and range of the original function $f(x)$:** - The domain of $f$ is the range of $f^{-1}$, so domain of $f$ is $\{1, -5, 10, 0, 6\}$. - The range of $f$ is the domain of $f^{-1}$, so range of $f$ is $\{-10, -8, -7, -6, 0\}$. 5. **Summary:** - Domain of $f$: $\{1, -5, 10, 0, 6\}$ - Range of $f$: $\{-10, -8, -7, -6, 0\}$ This is because the inverse function reverses the input-output pairs of the original function.