Here's what I mean by visually obvious:
File:Young.png - Wikipedia, the free encyclopedia
Just put b=f(a) in that figure.
I'm having trouble proving an equation.
Take to be a continuous strictly increasing function with and let be its inverse. Then:
This should be visually obvious. The graph of divides the rectangle with vertices and in two.
In the proof, I would like not to assume differentiability (since the equation is obviously true non-smooth functions too)