Question 25
Let $f(x) = |2\{x\} - 1|$ where $\{x\}$ denotes the fractional part of $x.$ The number $n$ is the smallest positive integer such that the equation $$
nf(xf(x)) = x
$$ has at least $2012$ real solutions $x.$ What is $n?$
Note: the fractional part of $x$ is a real number $y = \{x\},$ such that $0 \le y \lt 1$ and $x - y$ is an integer.
nf(xf(x)) = x
$$ has at least $2012$ real solutions $x.$ What is $n?$
Note: the fractional part of $x$ is a real number $y = \{x\},$ such that $0 \le y \lt 1$ and $x - y$ is an integer.