If the graph of a function \( f(x) \) is in Quadrant II, this means that the function takes positive \( y \) values for negative \( x \) values.
The graph of its inverse \( f^{-1}(x) \) will swap the \( x \) and \( y \) coordinates of the points on the graph of the original function. Since the original function's graph is in Quadrant II, after swapping, the inverse will have negative \( y \) values for positive \( x \) values.
This places the graph of the inverse in Quadrant IV.
So the answer is:
Quadrant IV