Question

If f(x) and its inverse function, f–1(x), are both plotted on the same coordinate plane, what is their point of intersection?

On a coordinate plane, a curve opens down and to the right in quadrants 3 and 4 and then changes direction and curves up and to the left in quadrants 1 and 4. The curve crosses the y-axis at (0, negative 2), changes direction at (1, negative 1, and crosses the x-axis at (2, 0).

(0, –2)
(1, –1)
(2, 0)
(3, 3)

Answer 1

The graph of f^{-1} is the reflection of the graph of f across the line y = x, so any intersection must lie on y = x (i.e. satisfy y = x). Among the choices only (3, 3) lies on y = x.

Answer: (3, 3).