{c}

Let $u<v$ lie in $f([a,b])$, and put $x=g(u)$ and $y=g(v)$. Equality $x=y$ would imply $u=v$. If $x>y$, strict <monotonicity> of $f$ would give $u=f(x)>f(y)=v$. Both are impossible, so $x<y$. Therefore the <inverse function> $g$ is \b[<strictly increasing>].

Solution

Past exam of the mathematics course of the University of Oxford / 2017 / Prelims / Mathematics II / 4 / a / ii / Solution

 Solution (source code)