Final answer:
The point (7, -1) on the graph of f(x) corresponds to the point (-1, 7) on the graph of its inverse f^{-1}(x), meaning that answer c is correct.
Step-by-step explanation:
If the point (7, -1) lies on the graph of f(x), the corresponding point that must lie on the graph of the inverse function f^{-1}(x) would essentially swap the x and y coordinates, resulting in the point (-1, 7). Therefore, the correct answer is c. (-1, 7).
When dealing with functions and their inverses, if a point (a, b) is on the graph of the function, then the point (b, a) will be on the graph of the inverse function. This relationship stems from the definition of inverse functions, where f^{-1}(f(x)) = x and f(f^{-1}(y)) = y. In this case, if f(7) = -1, then f^{-1}(-1) must equal 7, demonstrating that the coordinates are reversed in the inverse.