if f(x) and its inverse function, f⁻¹(x), are both plotted on the same coordinate plane, what is their point…

Answer:

The point of intersection of a function (y = f(x)) and its inverse (y = f^{-1}(x)) lies on the line (y=x). To find the intersection point from the graph, we look for the point where the graph of (f(x)) crosses the line (y = x). From the given graph, it appears that the point of intersection of (f(x)) and (f^{-1}(x)) is ((3,3))

Explanation:

Step1: Recall property of inverse - function intersection

The graphs of (y = f(x)) and (y=f^{-1}(x)) are symmetric about the line (y = x). So their intersection points lie on (y = x), i.e., (x=y) at the intersection points.

Step2: Identify intersection point on graph

By observing the graph of (f(x)) and considering the line (y = x) (the line where (x) - coordinate and (y) - coordinate are equal), we can see that the curve of (f(x)) intersects the line (y=x) at the point ((3,3))