Problem - 3824
Let $f(x)=x^3 -x^2 -13x+24$. Find three pairs of $(x,y)$ such that if $y=f(x)$, then $x=f(y)$.
This is equivalent to solving $x=f(f(x))$. Clearly $x=f(x)$ is one solution to this equation, Hence we can solve $x=x^3-x^2-13x+24$ which leads to $x=2, 3, -4$.