R to R/Affine-linear/Barycentric combination/Exercise

Let ${}\psi \colon \mathbb {R} \rightarrow \mathbb {R}$ be a mapping of the form

${}\psi (x)=ax+b\,$

with certain ${}a,b\in \mathbb {R}$. Show directly that ${}\psi$ is compatible with barycentric combinations.

Create a solution