  We devote this work to the functional equation $\psi \circ g = g\circ \psi$,
where $\psi$ is an unknown function and $g$ is piecewise linear unimodal map,
which is topologically conjugated to the tent map. We will call such $\psi$
self-semiconjugations of $g$. Our the main results are the following:
  1. Suppose that there is a self-semiconjugation of $g$, whose tangent at $0$
is not a power of $2$, and suppose that all the kinks of $g$ are in the
complete pre-image of $0$. Then all the self-semiconjugations of $g$ are
piecewise linear.
  2. Suppose that all self-semiconjugations of $g$ are piecewise linear. Then
the conjugacy of $g$ and the tent map is piecewise linear.
