xyzhomework.com XYZ Homework Ace Al Tutor from Numerade Score on last try: 0 of 1 pts. See Details for more. Next question Get a similar question You can retry this question below For the following exercises, use the graph of
shown below Find
.
The Correct Answer and Explanation is:
-2
To find the value of f⁻¹(2), we need to interpret what the inverse function represents. The expression f⁻¹(2) asks for the input value, x, for which the function f has an output value of 2. In other words, we are looking for the x that satisfies the equation f(x) = 2.
We can find this value by examining the provided graph of the function y = f(x).
- Locate the Output Value: First, find the value 2 on the vertical axis (the y-axis). This represents the output of the function, f(x).
- Find the Point on the Graph: From y = 2 on the vertical axis, trace a horizontal line to the left until it intersects with the red line, which is the graph of the function f.
- Determine the Corresponding Input Value: Once you have found the point of intersection on the graph, trace a vertical line straight down to the horizontal axis (the x-axis). The value where this vertical line meets the x-axis is the input value that corresponds to the output of 2.
By following these steps on the given graph, we can see that the horizontal line at y = 2 intersects the function’s graph at the point where the x-value is -2. This means the point (-2, 2) lies on the graph of f.
Therefore, since f(-2) = 2, the definition of an inverse function tells us that f⁻¹(2) = -2.
