Consider the tent map defined on $[0, 1]$: $$f(x) = 2x, \; 0<x<\frac{1}{2} \;\; and \;\; f(x) = 2(1-x), \; \frac{1}{2} \leq x \leq 1.$$
I showed that $f$ is topological conjugate with $F(x) = 4x(1-x)$.
Are there other quadratic functions $F_\alpha(x) = \alpha x(1-x)$ for which $f$ is topological conjugate?.
Can someone give me a hint?
Thank you!