Past exam of the mathematics course of the University of Cambridge / 2008 / ia / Paper 1 / 10D / c / ii

The continuous functionhas the required image. Its values are nonnegative, and for every $y\ge 0$ the point $x=1/(y+1)\in (0,1]$ satisfies $f(x)=y$. Thus the image is exactly $[0,\infty )$. The missing left endpoint permits unboundedness without a failure of continuity on the domain.