Mathegoras

Functions › Functional equations › Extremes in functional equations

Smallest n with many solutions

High school · ●●●●○ 100 pts

Let f(x)=∣2{x}−1∣f(x)=|2\{x\}-1|, where {x}\{x\} denotes the fractional part of xx. Find the smallest positive integer nn such that the equation nf(xf(x))=xn f(x f(x))=x has at least 20122012 real solutions.

Sign in to save your progress.

fractional partpiecewise functionscounting solutionscounting intersection points