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 / iii

It is surjective but not injective; there is no global inverse function. Noninjectivity follows fromFor surjectivity, restrict to $x<1$, whereThis restriction is a continuous function, tends to $-\infty$ as $x\to -\infty$ and to $+\infty$ as $x\to 1^{-}$. The intermediate value theorem therefore supplies a preimage for every real number. The additional branch $x>1$ destroys global injectivity but cannot destroy surjectivity.