$T(x)=\begin{array}{lr}\ 2x, x \in [0,\frac{1}{2}] \\ 2-2x, x\in [\frac{1}{2},1] \end{array}$ and $F_4(x)=4x(1-x)$ with conjugacy $h(x)=\sin^2(\frac{\pi x}{2})$
I am completely lost, these two things clearly do not follow $f\cdot h (x)= h \cdot g (x)$
As $f(h(x))= 4\cos^2(\pi x /2)\sin^2(\pi x / 2)$ and $h(T(x)) = \sin^2 (\pi x) \mbox{ for } x \in [0,\frac{1}{2}] \mbox{ and } \sin^2(\pi (1-x)) \mbox{ for } x\in [1/2,1]$
Where have I gone wrong?