How to solve cos(2nx)=cos(x) I am given the function F:R→R , x↦4x(1−x) and I have...
How to solve
I am given the function , and I have to find all n-cycles of the function. I have already reduced this to the problem of solving for . Using Mathematica and , I concluded that the solutions must be . Since the equation obviously has solutions and the solution set has elements, it only remains to verify that they are indeed solutions to the equation. I tried using and proving this by induction on n, but I was not able to.