Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Discrete mathematics, continuous mathematics, and probability / 1 / c / i

The function is injective and surjective, with inverse function $f^{-1}(y)=1-y$. Equality $1-x=1-x^{\prime }$ forces $x=x^{\prime }$. For any $y\in (0,1)$, the input $x=1-y$ also lies in $(0,1)$ and satisfies $f(x)=y$. Applying the function twice returns the original input.