I wonder the following property hold but I am unable to prove it. Can anyone help me !
Given functions $f,g: \mathbb{R}\to \mathbb{R}$. Assume that $f$ be piece-wise linear and g is convex/concave. What kind of conditions on function $f$ to make composition function $g\circ f$ is convex/concave?
Its easy to check if $f$ is linear with second derivative but here the problem is that function $f$ is not differentiable.