For every real number \(x\) , let \(\lfloor x \rfloor\) denote the greatest integer not exceeding \(x\) , and let \(f(x)=\lfloor x\rfloor(2014^{x-\lfloor x\rfloor}-1). \) The set of all numbers \(x\) such that \(1\leq x<2014 \) and \(f(x)\leq 1\) is a union of disjoint intervals. What is the sum of the lengths of those intervals?
I only have one attempt left! The answer is NOT 1/2
