Easy question

["Mukhtar Bekkali"]

Function f=x^n, 0<x<1 and n>1 and f=(1-x)^n are mirror images of each
other around x=1/2. Can you suggest a function that is a mirror image
of f=x^n around f=x. For example, in 1x1 square I need to find a
function that describes the mirror image of f=x^n around diagonal. This
new function has to be increasing and concave. I am tired and my brain
has stopped functioning for today. Please solve this problem for me.
Thx.