\b[No such continuous function exists.] The <extreme value theorem> makes every <continuous function> on the <closed interval> $[0,1]$ bounded and gives it a finite maximum. Its image therefore cannot equal the unbounded <real interval> $[0,\infty)$.

Solution

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

 Solution (source code)