Past exam of the mathematics course of the University of Cambridge / 2013 / ia / Paper 1 / 10E / b / i / Solution

If $f$ is a strictly increasing function and $x\ne y$, one of $x<y$ or $y<x$ holds. The corresponding strict inequality of function values shows that $f$ is injective. Conversely, if $f(x)<f(y)$, then $x=y$ is impossible and $x>y$ would imply $f(x)>f(y)$. ThusTogether with strict increase, this says that such a function preserves and reflects the ordering of points.