What is "f"? How is it necessary for this exercise?

Yourformattingis ambiguous. Do you mean the following?

. . . . .

The domain of g is given to you in the exercise. The range (the "image set") of g-inverse will be the domain of g, by definition of "inverse". The domain of g-inverse will be the range of g, which you can "see" from the graph of g.

To learn how to find the inverse of a function, tryhere. If you get stuck, kindly please reply with a clarification of the function g, along with a clear listing of your steps and reasoning so far.

Thank you!