Question 21
For every real number $x,$ let $\lfloor x\rfloor$ denote the greatest integer not exceeding $x,$ and let $$
f(x)=\lfloor x\rfloor\left(2014^{\,x-\lfloor x\rfloor}-1\right).
$$ The set of all numbers $x$ such that $1\le x\lt2014$ and $f(x)\le1$ is a union of disjoint intervals. What is the sum of the lengths of those intervals?
f(x)=\lfloor x\rfloor\left(2014^{\,x-\lfloor x\rfloor}-1\right).
$$ The set of all numbers $x$ such that $1\le x\lt2014$ and $f(x)\le1$ is a union of disjoint intervals. What is the sum of the lengths of those intervals?