Use the above graph of f(x) to complete the following table for values of its inverse function, f^{-1}(x).

The graph has a point on (2,2)the y-intercept is 4 the x intercept is 3

x =-4, 8, 0, -2, 2
f^{-1}(x)


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To find the values of the inverse function, f^{-1}(x), we need to switch the x and y coordinates. The given graph has a point on (2,2), which means that f(2) = 2. So, the inverse function f^{-1}(2) = 2.

To find the y-intercept of the graph, we need to find the value of x when y = 0. From the graph, we can see that when y = 0, x = 4. So, the inverse function f^{-1}(0) = 4.

To find the x-intercept of the graph, we need to find the value of y when x = 0. From the graph, we can see that when x = 0, y = 3. So, the inverse function f^{-1}(3) = 0.

Now, let's find the values of the inverse function for the given x values:

For x = -4, we can see from the graph that the corresponding y value is 5. So, f^{-1}(-4) = 5.

For x = 8, we can see from the graph that the corresponding y value is 1. So, f^{-1}(8) = 1.

For x = 0, we already found that the corresponding y value is 4. So, f^{-1}(0) = 4.

For x = -2, we can see from the graph that the corresponding y value is 4. So, f^{-1}(-2) = 4.

For x = 2, we already found that the corresponding y value is 2. So, f^{-1}(2) = 2.



Therefore, the completed table for values of the inverse function, f^{-1}(x), is:

x | f^{-1}(x)
------------
-4 | 5
8 | 1
0 | 4
-2 | 4
2 | 2