Inverse of a function is reverse mapping (if possible). The completed table would look like as shown below:
What is inverse of a function?
Suppose that the given function is [tex]f: X \rightarrow Y[/tex]
Then, if function 'f' is one-to-one and onto function(a needed condition for inverses to exist), then, the inverse of the considered function is [tex]f^{-1}: Y \rightarrow X[/tex] such that:
[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex] (and vice versa).
It simply means,inverse of 'f' is undo operator, that takes back the effect of 'f'
Inverse of inverse function is function itself.
For the given case, if the function (take x = -2) maps x = -2 to f(x) = -28, then the inverse of this function will take back -28 to -2.
This logic tells us that:
[tex]\begin{array}{cccccc}x&-28&-9&-2&-1&0\\f^{-1}(x)&-2&1&0&1&2\end{array}[/tex]
(x simply denotes input). For inverse function, those values which were outputs of [tex]f(x)[/tex] are now going to serve as input to inverse of [tex]f(x)[/tex] which is [tex]f^{-1}(x)[/tex]
Thus, the completed table would look like:
[tex]\begin{array}{cccccc}x&-28&-9&-2&-1&0\\f^{-1}(x)&-2&1&0&1&2\end{array}[/tex]
Learn more about inverse functions here:
https://brainly.com/question/21527869
