\b[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>.

Solution

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

 Solution (source code)