Questions: Given the graph of (f(x)) shown, answer the following. (a) What is (f^-1(-2)) ? (b) Solve the equation (f(x)=-11). What is (f^-1(-11)) ? (c) Sketch the graph of the inverse function.

Solution Steps

The value of f⁻¹(-2) is the x-value where f(x) = -2. Looking at the graph, f(x) = -2 when x = -1.

We are looking for the x-value where f(x) = -11. From the graph, this occurs at x = -3. Since f(-3) = -11, then f⁻¹(-11) = -3.

To sketch the inverse function, reflect the graph of f(x) across the line y = x. This means swapping the x and y coordinates of each point on the original graph. Key points on f(x) are approximately (-3, -11), (-1, -2), (2, -2), and (4,14). The corresponding points on f⁻¹(x) would be (-11, -3), (-2, -1), (-2, 2), and (14, 4). Plot these points and draw a curve through them, maintaining the general shape of the original function reflected.

Final Answer: