1. **State the problem:** We are given a function $f$ with points on its graph and asked to find values and solve equations involving $f$ and its inverse $f^{-1}$. 2. **Given points:** - $f(-2) = 8$ - $f(-7) = -6$ 3. **Part a:** Find $f(-2)$. - From the given, $f(-2) = 8$. 4. **Part b:** Solve $f(x) = -7$. - We look for $x$ such that $f(x) = -7$. - From the graph description, the curve crosses $y = -7$ near $x = -7$ but $f(-7) = -6$, so no exact point given. - Since $f(-7) = -6$ and the curve decreases near $x=-7$, $f(x) = -7$ likely has no solution or is not given explicitly. 5. **Part c:** How many solutions are there to $f^{-1}(x) = -5$? - $f^{-1}(x) = -5$ means $x = f(-5)$. - We need to find how many $x$ satisfy $f^{-1}(x) = -5$, i.e., how many $x$ satisfy $x = f(-5)$. - This is equivalent to finding the value of $f(-5)$. - Since the graph is not fully described at $x=-5$, we cannot determine the exact value or number of solutions. 6. **Summary:** - $f(-2) = 8$ (given). - $f(-7) = -6$ (given). - No explicit solution for $f(x) = -7$ from given data. - Number of solutions to $f^{-1}(x) = -5$ cannot be determined from given data. **Final answers:** - a) $f(-2) = 8$ - b) No solution given for $f(x) = -7$ - c) Cannot determine number of solutions for $f^{-1}(x) = -5$ from given information.