I am currently going over some example questions for my dynamical systems module and I am wondering how to calculate the entropy of certain maps.
The maps in question are $$T:[0,1] \to [0,1] \hspace{0.2cm} \text{defined by} \hspace{0.2cm} T(x)=|2x-1|$$ $$T : [0,1] \to [0,1] \hspace{0.2cm} \text{defined by} \hspace{0.2cm} T(x)=4x(1-x). $$ Now from the definition of entropy based on $(n,\varepsilon)$-separated or $(n,\varepsilon)$-spanning sets this seems unreasonable, and I found the answer used a comparison to the full shift map on $2$ symbols, by knowing that each of these maps is semi-conjugate to the full shift map on $2$ symbols and hence has the same entropy, which is the log of the dominant eigenvalue of $A= \begin{bmatrix} 1 & 1\\ 1 & 1 \end{bmatrix}$, giving $h(T)=\log 2$.
My issue is that I'm unsure how I would be able to come up with a map that was semi-conjugate to the given maps, and even now I am unsure how to see that the full shift on $2$ symbols is conjugate to each of these maps.
Any insight or explanation would be appreciated thanks :)