Question

Consider the graphs of the two functions:



Which rationale best describes why the functions are inverses?

The functions intersect each other.
The functions have the same general curve.
The functions are reflections over the line y = x.
One function has an x-intercept and the other has a y-intercept.

Answer 1

The functions are reflections over the line y = x.

Reason: If g is the inverse of f then every point (a,b) on f corresponds to (b,a) on g, so the graphs are mirror images across y = x (and any intersection points lie on y = x).