Final answer:
The values of f^-1 for given y-values cannot be determined without the graph of function f. For a graph that shows f(x), the x-value corresponding to each given y-value on the graph represents f⁻¹⁽ʸ⁾. If the function is not one-to-one, it may not have an inverse that is also a function without restricting its domain.
Step-by-step explanation:
Without the provided graph of the function f, it is not possible to accurately determine the values of f-1 (the inverse function of f). The inverse function, f-1, effectively reverses the operation of f, meaning for f-1(y), we are looking for the value of x such that f(x) = y. To find the values of the inverse function from the graph, you would look for the corresponding x-values on the graph where the function's y-values are equal to the specified values.
For example:
- To find f-1(-4), locate -4 on the y-axis, find the corresponding point(s) on the graph, and observe the x-value(s) at that point.
- Repeat this process to find f-1(-3), f-1(0), f-1(2), and f-1(4).
If the graph is not one-to-one, meaning that for some y-values there is more than one corresponding x-value, the function f does not have an inverse function that is also a function. To remedy this for instructional purposes, it's common to restrict the domain of f so that f is one-to-one and therefore does have an inverse that is also a function.