Question 6
Let $$f(x)=\frac{2x^3-3}{3(x^2-1)}.$$ 1. Prove that there exists a function $g$ continuous on $\mathbb R$ such that $f(g(x))=x$ and $g(x)>x$ for every real $x$. 2. Prove that there exists a real $a>1$ such that the sequence $a_0=a$, $a_{n+1}=f(a_n)$ for every integer $n\ge0$ is periodic with least positive period $1995$. The rational function has its natural domain $\mathbb R\setminus\{-1,1\}$.
Essay grading is manual; the rubric is editorial. Importer multipliers: correct 1, incorrect 0, blank 0.
Essay grading is manual; the rubric is editorial. Importer multipliers: correct 1, incorrect 0, blank 0.