Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Discrete mathematics, continuous mathematics, and probability resit / 1 / b / ii / Solution

Both injective and surjective. The natural logarithm is strictly increasing on the positive real numbers, so it is injective. For every $y\in \mathbb{R}$, $x=e^y>0$ satisfies $\ln x=y$; hence the function is surjective, with the exponential function as its inverse function.