# How to find $f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$

Discussion in 'Mathematics' started by John Doe, Oct 8, 2018.

1. ### John DoeGuest

How can I determine $f(x)$ if $f(1-f(x))=x$ for all real $x$? I have already recognized one problem caused from this: it follows that $f(f(x))=1-x$, which is discontinuous. So how can I construct a function $f(x)$?

Best regards and thanks, John